DenysMedvid/pdf2htmlEX
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pdf2htmlEX/demo/cheat10.page
Lu Wang 2d8df9d647 update demo
2013-09-28 13:30:57 +08:00

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class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Theoretical<span class="_ _0"> </span>Computer<span class="_ _0"> </span>Science<span class="_ _0"> </span>Cheat<span class="_ _0"> </span>Sheet</div><div class="t m0 xf7 h3 y2 ff2 fs0 fc0 sc0 ls0 ws0">Series<span class="_ _94"> </span>Esc<span class="_ _5"></span>her’s Knot</div><div class="t m0 x1ba h3 y3 ff2 fs0 fc0 sc0 ls0 ws0">Expansions:</div><div class="t m0 x92 h3 y544 ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 x1c9 h4 y5e7 ff2 fs0 fc0 sc0 ls0 ws0">(1<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff3">x</span></span>)</div><div class="t m0 x1ca h5 y34c ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff5">+1</span></div><div class="t m0 xe2 h3 y5e8 ff2 fs0 fc0 sc0 ls0 ws0">ln</div><div class="t m0 xe5 h3 y544 ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 xe3 h4 y5e7 ff2 fs0 fc0 sc0 ls0 ws0">1<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff3">x</span></span></div><div class="t m0 x94 h3 y5e9 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x1af h5 y495 ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 x1a6 h6 y5ea ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x1a6 h5 y5eb ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=0</span></div><div class="t m0 x145 h3 y5e8 ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff3">H</span></div><div class="t m0 xd6 h5 y5ec ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff5">+</span>i</div><div class="t m0 x129 h4 y5e8 ff4 fs0 fc0 sc0 ls0 ws0">−<span class="_ _8"> </span><span class="ff3">H</span></div><div class="t m0 x12a h5 y5ec ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x1b8 h3 y5e8 ff2 fs0 fc0 sc0 ls0 ws0">)</div><div class="t m0 xc9 h6 yb ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x8e h3 y544 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _8"> </span><span class="ff2">+<span class="_ _8"> </span></span>i</div><div class="t m0 x192 h3 y5ed ff3 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x8 h6 yb ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x150 h3 y5e8 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x157 h5 y5ee ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 xe9 h3 y5e8 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x9c h6 yb ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x46 h3 y544 ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 x46 h3 y5e7 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x9d h6 yb ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x2b h5 y576 ff8 fs1 fc0 sc0 ls0 ws0">−<span class="ff6">n</span></div><div class="t m0 x2c h3 y5e8 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x10e h5 y495 ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 xac h6 y5ea ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x15c h5 y5eb ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=0</span></div><div class="t m0 x10 h6 yb ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x2e h3 y544 ff3 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x2e h3 y5e7 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x14 h6 yb ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x1cb h3 y5e8 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x2f h5 y5ee ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x3f h3 y5e8 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x1a3 h3 y19 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 xfc h5 y11 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x94 h3 y19 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x1af h5 y14a ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 x1a6 h6 y23c ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x1a6 h5 y14c ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=0</span></div><div class="t m0 x1a0 h6 y10 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x10c h3 y51 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x103 h3 y436 ff3 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x1c3 h6 y10 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x83 h3 y19 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x13c h5 y11 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x129 h3 y19 ff3 fs0 fc0 sc0 ls0 ws0">,<span class="_ _95"> </span><span class="ff2">(</span>e</div><div class="t m0 x16f h5 y11 ff6 fs1 fc0 sc0 ls0 ws0">x</div><div class="t m0 x73 h4 y19 ff4 fs0 fc0 sc0 ls0 ws0">−<span class="_ _8"> </span><span class="ff2">1)</span></div><div class="t m0 x67 h5 y11 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x2c h3 y19 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x10e h5 y14a ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 xac h6 y23c ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x15c h5 y14c ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=0</span></div><div class="t m0 x10 h6 y10 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x2e h3 y51 ff3 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x2e h3 y436 ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x14 h6 y10 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x3e h3 y51 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="ff2">!</span>x</div><div class="t m0 x40 h5 y5ef ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x195 h3 y436 ff3 fs0 fc0 sc0 ls0 ws0">i<span class="ff2">!</span></div><div class="t m0 x41 h3 y5f0 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x1a9 h6 y5f1 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x92 h3 y12f ff2 fs0 fc0 sc0 ls0 ws0">ln</div><div class="t m0 xfc h3 y14d ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 xe1 h4 y14f ff2 fs0 fc0 sc0 ls0 ws0">1<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff3">x</span></span></div><div class="t m0 x106 h6 y5f2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xf1 h5 y5f3 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x94 h3 y12f ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x1af h5 y2f2 ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 x1a6 h6 y5f4 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x1a6 h5 y5f5 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=0</span></div><div class="t m0 x1a0 h6 y5f2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x103 h3 y14d ff3 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x10c h3 y14f ff3 fs0 fc0 sc0 ls0 ws0">n</div><div class="t m0 x1c3 h6 y5f2 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x97 h3 y14d ff3 fs0 fc0 sc0 ls0 ws0">n<span class="ff2">!</span>x</div><div class="t m0 x1bd h5 y13 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x14c h3 y14f ff3 fs0 fc0 sc0 ls0 ws0">i<span class="ff2">!</span></div><div class="t m0 x89 h3 y12f ff3 fs0 fc0 sc0 ls26 ws0">,x<span class="_ _96"></span><span class="ff2 ls0">cot<span class="_ _6"> </span><span class="ff3">x<span class="_ _65"> </span></span>=</span></div><div class="t m0 x10e h5 y2f2 ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 xac h6 y5f4 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x15c h5 y5f5 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=0</span></div><div class="t m0 x10 h4 y14d ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff4">−</span>4)</div><div class="t m0 x198 h5 y13 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x3e h3 y14d ff3 fs0 fc0 sc0 ls0 ws0">B</div><div class="t m0 x11c h5 y5f6 ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">i</span></div><div class="t m0 x40 h3 y14d ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x13a h5 y13 ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">i</span></div><div class="t m0 x5d h3 y14f ff2 fs0 fc0 sc0 ls0 ws0">(2<span class="ff3">i</span>)!</div><div class="t m0 x4b h3 y12f ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x1ca h3 y5f7 ff2 fs0 fc0 sc0 ls0 ws0">tan<span class="_ _6"> </span><span class="ff3">x<span class="_ _13"> </span></span>=</div><div class="t m0 x1af h5 y579 ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 x1a6 h6 y131 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x1a6 h5 y5a ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 x145 h4 y5f8 ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff4">−</span>1)</div><div class="t m0 x83 h5 y133 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff8">−<span class="ff5">1</span></span></div><div class="t m0 x14d h3 y43a ff2 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 x89 h5 y20 ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">i</span></div><div class="t m0 x12a h3 y43a ff2 fs0 fc0 sc0 ls0 ws0">(2</div><div class="t m0 xc9 h5 y20 ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">i</span></div><div class="t m0 xf7 h4 y43a ff4 fs0 fc0 sc0 ls0 ws0">−<span class="_ _8"> </span><span class="ff2">1)<span class="ff3">B</span></span></div><div class="t m0 x150 h5 y5f9 ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">i</span></div><div class="t m0 x174 h3 y43a ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x11b h5 y20 ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">i<span class="ff8">−</span></span>1</div><div class="t m0 x171 h3 y5fa ff2 fs0 fc0 sc0 ls0 ws0">(2<span class="ff3">i</span>)!</div><div class="t m0 x154 h3 y5fb ff3 fs0 fc0 sc0 ls27 ws0">,ζ<span class="_ _97"></span><span class="ff2 ls0">(<span class="ff3">x</span><span class="ls28">)=</span></span></div><div class="t m0 x10e h5 y579 ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 xac h6 y131 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x15c h5 y5a ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 xb5 h3 y43a ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 x10 h3 y5fa ff3 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 xaf h5 y50c ff6 fs1 fc0 sc0 ls0 ws0">x</div><div class="t m0 x1b5 h3 y5f8 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x87 h3 y50f ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 xe1 h3 y338 ff3 fs0 fc0 sc0 ls0 ws0">ζ<span class="_ _15"></span><span class="ff2">(</span>x<span class="ff2">)</span></div><div class="t m0 x94 h3 y5d ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x1af h5 y5fc ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 x1a6 h6 y331 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x1a6 h5 y13f ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 xd5 h3 y50f ff3 fs0 fc0 sc0 ls0 ws0">µ<span class="ff2">(</span>i<span class="ff2">)</span></div><div class="t m0 x10c h3 y338 ff3 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 xfd h5 y335 ff6 fs1 fc0 sc0 ls0 ws0">x</div><div class="t m0 x104 h3 y5d ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x1bb h4 y50f ff3 fs0 fc0 sc0 ls0 ws0">ζ<span class="_ _15"></span><span class="ff2">(</span>x<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1)</span></span></div><div class="t m0 x46 h3 y338 ff3 fs0 fc0 sc0 ls0 ws0">ζ<span class="_ _15"></span><span class="ff2">(</span>x<span class="ff2">)</span></div><div class="t m0 x2c h3 y5d ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x10e h5 y5fc ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 xac h6 y331 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x15c h5 y13f ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 x10 h3 y50f ff3 fs0 fc0 sc0 ls0 ws0">φ<span class="ff2">(</span>i<span class="ff2">)</span></div><div class="t m0 xae h3 y338 ff3 fs0 fc0 sc0 ls0 ws0">i</div><div class="t m0 x2e h5 y335 ff6 fs1 fc0 sc0 ls0 ws0">x</div><div class="t m0 x12c h3 y5d ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x2f h3 y32 ff2 fs0 fc0 sc0 ls0 ws0">Stieltjes In<span class="_ _5"></span>tegration</div><div class="t m0 xe1 h3 y158 ff3 fs0 fc0 sc0 ls0 ws0">ζ<span class="_ _15"></span><span class="ff2">(</span>x<span class="ff2 ls29">)=</span></div><div class="t m0 x10a h6 y142 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x8c h5 y5fd ff6 fs1 fc0 sc0 ls0 ws0">p</div><div class="t m0 xd6 h3 y5fe ff2 fs0 fc0 sc0 ls0 ws0">1</div><div class="t m0 x124 h4 y260 ff2 fs0 fc0 sc0 ls0 ws0">1<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff3">p</span></span></div><div class="t m0 x83 h5 y5ff ff8 fs1 fc0 sc0 ls0 ws0">−<span class="ff6">x</span></div><div class="t m0 x1aa h3 y158 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 xc5 h3 y600 ff3 fs0 fc0 sc0 ls0 ws0">ζ</div><div class="t m0 x1a3 h5 y343 ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x87 h3 y601 ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff3">x</span><span class="ls2a">)=</span></div><div class="t m0 x1a6 h5 y2ca ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 x10a h6 y25c ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x10a h5 y3a ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 x145 h3 y359 ff3 fs0 fc0 sc0 ls0 ws0">d<span class="ff2">(</span>i<span class="ff2">)</span></div><div class="t m0 x128 h3 y4aa ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x103 h5 y602 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x13c h3 y601 ff2 fs0 fc0 sc0 ls0 ws0">where <span class="ff3">d</span>(<span class="ff3">n</span><span class="ls1">)=</span></div><div class="t m0 x179 h6 y458 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x157 h5 y62 ff6 fs1 fc0 sc0 ls0 ws0">d<span class="ff8">|</span>n</div><div class="t m0 xfa h3 y601 ff2 fs0 fc0 sc0 ls0 ws0">1<span class="ff3">,</span></div><div class="t m0 x84 h4 y603 ff3 fs0 fc0 sc0 ls0 ws0">ζ<span class="_ _15"></span><span class="ff2">(</span>x<span class="ff2">)</span>ζ<span class="_ _2"></span><span class="ff2">(</span>x<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"></span><span class="ff2">1)<span class="_ _64"> </span>=</span></span></div><div class="t m0 x1a6 h5 y64 ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 x10a h6 y3f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x10a h5 y46 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 x145 h3 y67 ff3 fs0 fc0 sc0 ls0 ws0">S<span class="_ _15"></span><span class="ff2">(</span>i<span class="ff2">)</span></div><div class="t m0 x14a h3 y604 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x1ae h5 y605 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x129 h3 y606 ff2 fs0 fc0 sc0 ls0 ws0">where <span class="ff3">S<span class="_ _15"></span></span>(<span class="ff3">n</span><span class="ls1">)=</span></div><div class="t m0 xe8 h6 y1ef ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xe9 h5 y5ce ff6 fs1 fc0 sc0 ls0 ws0">d<span class="ff8">|</span>n</div><div class="t m0 x155 h3 y606 ff3 fs0 fc0 sc0 ls0 ws0">d,</div><div class="t m0 xc5 h3 y6c ff3 fs0 fc0 sc0 ls0 ws0">ζ<span class="_ _15"></span><span class="ff2">(2</span>n<span class="ff2 ls2b">)=</span></div><div class="t m0 x10a h3 y1ad ff2 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 x117 h5 y15e ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">n<span class="ff8">−</span></span>1</div><div class="t m0 x10c h4 y1ad ff4 fs0 fc0 sc0 ls0 ws0">|<span class="ff3">B</span></div><div class="t m0 xd7 h5 y54d ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">n</span></div><div class="t m0 x14c h4 y1ad ff4 fs0 fc0 sc0 ls0 ws0">|</div><div class="t m0 xf5 h3 y78 ff2 fs0 fc0 sc0 ls0 ws0">(2<span class="ff3">n</span>)!</div><div class="t m0 x10d h3 y6c ff3 fs0 fc0 sc0 ls0 ws0">π</div><div class="t m0 x1b0 h5 y446 ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">n</span></div><div class="t m0 x12a h4 y6c ff3 fs0 fc0 sc0 ls3 ws0">,n<span class="_ _a"></span><span class="ff4 ls0">∈<span class="_ _7"> </span><span class="ff9">N<span class="ff3">,</span></span></span></div><div class="t m0 x87 h3 y75 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 xe1 h3 y368 ff2 fs0 fc0 sc0 ls0 ws0">sin<span class="_ _6"> </span><span class="ff3">x</span></div><div class="t m0 x6 h3 y303 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x1a6 h5 y607 ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 x10a h6 y608 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x10a h5 y168 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=0</span></div><div class="t m0 x82 h4 y303 ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff4">−</span>1)</div><div class="t m0 x118 h5 y3bd ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff8">−<span class="ff5">1</span></span></div><div class="t m0 x10d h3 y75 ff2 fs0 fc0 sc0 ls0 ws0">(4</div><div class="t m0 x89 h5 y4b3 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x13d h4 y75 ff4 fs0 fc0 sc0 ls0 ws0">−<span class="_ _8"> </span><span class="ff2">2)<span class="ff3">B</span></span></div><div class="t m0 x192 h5 y527 ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">i</span></div><div class="t m0 x7 h3 y75 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 xda h5 y4b3 ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">i</span></div><div class="t m0 x5 h3 y368 ff2 fs0 fc0 sc0 ls0 ws0">(2<span class="ff3">i</span>)!</div><div class="t m0 xdc h3 y303 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x3 h6 y1f9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x85 h4 y414 ff2 fs0 fc0 sc0 ls0 ws0">1<span class="_ _8"> </span><span class="ff4">−</span></div><div class="t m0 x9a h4 y1f9 ff4 fs0 fc0 sc0 ls0 ws0">√</div><div class="t m0 x140 h4 y414 ff2 fs0 fc0 sc0 ls0 ws0">1<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span></span>4<span class="ff3">x</span></div><div class="t m0 x18d h3 y1b8 ff2 fs0 fc0 sc0 ls0 ws0">2<span class="ff3">x</span></div><div class="t m0 x107 h6 y1f9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x141 h5 yaa ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x6 h3 y609 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x1a6 h5 yaa ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 x10a h6 ya9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x10a h5 y3c4 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=0</span></div><div class="t m0 x145 h4 y414 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="ff2">(2</span>i<span class="_ _8"> </span><span class="ff2">+<span class="_ _8"> </span></span>n<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff2">1)!</span></span></div><div class="t m0 xfd h3 y1b8 ff3 fs0 fc0 sc0 ls0 ws0">i<span class="ff2">!(</span>n<span class="_ _8"> </span><span class="ff2">+<span class="_ _8"> </span></span>i<span class="ff2">)!</span></div><div class="t m0 x11a h3 y60a ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 xf6 h5 y26d ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 xca h3 y609 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x8f h3 yae ff3 fs0 fc0 sc0 ls0 ws0">e</div><div class="t m0 x1ca h5 y8e ff6 fs1 fc0 sc0 ls0 ws0">x</div><div class="t m0 x140 h3 yae ff2 fs0 fc0 sc0 ls0 ws0">sin<span class="_ _6"> </span><span class="ff3">x<span class="_ _33"> </span></span>=</div><div class="t m0 x1a6 h5 y60b ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 x10a h6 y2cf ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x10a h5 y59e ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=1</span></div><div class="t m0 x145 h3 y60c ff2 fs0 fc0 sc0 ls0 ws0">2</div><div class="t m0 x14a h5 y28f ff6 fs1 fc0 sc0 ls0 ws0">i/<span class="ff5">2</span></div><div class="t m0 x118 h3 y60c ff2 fs0 fc0 sc0 ls0 ws0">sin</div><div class="t m0 x1aa h5 y60d ff6 fs1 fc0 sc0 ls0 ws0">iπ</div><div class="t m0 x14d h5 yaf ff5 fs1 fc0 sc0 ls0 ws0">4</div><div class="t m0 x118 h3 y60e ff3 fs0 fc0 sc0 ls0 ws0">i<span class="ff2">!</span></div><div class="t m0 xd8 h3 yae ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 xd9 h5 y8e ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x1b8 h3 yae ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x85 h6 y1ca ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x1ab h4 y60f ff2 fs0 fc0 sc0 ls0 ws0">1<span class="_ _8"> </span><span class="ff4">−</span></div><div class="t m0 x87 h4 y96 ff4 fs0 fc0 sc0 ls0 ws0">√</div><div class="t m0 x88 h4 y60f ff2 fs0 fc0 sc0 ls0 ws0">1<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span><span class="ff3">x</span></span></div><div class="t m0 x1b4 h3 y610 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x6 h3 y611 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x1a6 h5 y1cb ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 x10a h6 y1c9 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x10a h5 y532 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=0</span></div><div class="t m0 x10d h3 y60f ff2 fs0 fc0 sc0 ls0 ws0">(4<span class="ff3">i</span>)!</div><div class="t m0 x145 h3 y612 ff2 fs0 fc0 sc0 ls0 ws0">16</div><div class="t m0 x1ae h5 yb3 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 xd6 h4 y95 ff4 fs0 fc0 sc0 ls0 ws0">√</div><div class="t m0 x104 h3 y612 ff2 fs0 fc0 sc0 ls0 ws0">2(2<span class="ff3">i</span>)!(2<span class="ff3">i<span class="_ _8"> </span></span>+<span class="_ _8"> </span>1)!</div><div class="t m0 x136 h3 y611 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x179 h5 y613 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x150 h3 y611 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x84 h6 y17a ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xc7 h3 y53e ff2 fs0 fc0 sc0 ls0 ws0">arcsin<span class="_ _6"> </span><span class="ff3">x</span></div><div class="t m0 xc6 h3 y614 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x106 h6 y17a ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x130 h5 y615 ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x6 h3 y2d3 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x1a6 h5 y17b ff8 fs1 fc0 sc0 ls0 ws0">∞</div><div class="t m0 x10a h6 y294 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x10a h5 y5a5 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">=0</span></div><div class="t m0 x97 h3 y53e ff2 fs0 fc0 sc0 ls0 ws0">4</div><div class="t m0 x14c h5 y616 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x10d h3 y53e ff3 fs0 fc0 sc0 ls0 ws0">i<span class="ff2">!</span></div><div class="t m0 x134 h5 y616 ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x145 h3 y614 ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff3">i<span class="_ _8"> </span></span>+<span class="_ _8"> </span>1)(2<span class="ff3">i<span class="_ _8"> </span></span>+<span class="_ _8"> </span>1)!</div><div class="t m0 xf7 h3 y2d3 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 xca h5 y617 ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">i</span></div><div class="t m0 xcb h3 y2d3 ff3 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 xef h3 y342 ff2 fs0 fc0 sc0 ls0 ws0">If <span class="ff3">G </span>is con<span class="_ _5"></span>tinuous in the in<span class="_ _5"></span>terv<span class="_ _5"></span>al [<span class="ff3">a,<span class="_ _6"> </span>b</span>] and <span class="ff3">F<span class="_ _1e"> </span></span>is nondecreasing then</div><div class="t m0 x13a h6 y458 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x31 h5 y4a9 ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 x10f h5 y618 ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 x30 h3 y619 ff3 fs0 fc0 sc0 ls0 ws0">G<span class="ff2">(</span>x<span class="ff2">)<span class="_ _6"> </span></span>dF<span class="_ _6"> </span><span class="ff2">(</span>x<span class="ff2">)</span></div><div class="t m0 xef h4 y61a ff2 fs0 fc0 sc0 ls0 ws0">exists.<span class="_ _34"> </span>If <span class="ff3">a<span class="_ _7"> </span><span class="ff4">≤<span class="_ _7"> </span></span>b<span class="_ _7"> </span><span class="ff4">≤<span class="_ _7"> </span></span>c </span>then</div><div class="t m0 x178 h6 y603 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xab h5 y5ce ff6 fs1 fc0 sc0 ls0 ws0">c</div><div class="t m0 x5c h5 y15d ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 x170 h3 y69 ff3 fs0 fc0 sc0 ls0 ws0">G<span class="ff2">(</span>x<span class="ff2">)<span class="_ _6"> </span></span>dF<span class="_ _6"> </span><span class="ff2">(</span>x<span class="ff2 ls1">)=</span></div><div class="t m0 x41 h6 y603 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x9f h5 y5ce ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 x42 h5 y15d ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 x30 h3 y69 ff3 fs0 fc0 sc0 ls0 ws0">G<span class="ff2">(</span>x<span class="ff2">)<span class="_ _6"> </span></span>dF<span class="_ _6"> </span><span class="ff2">(</span>x<span class="ff2 ls9">)+</span></div><div class="t m0 x1a h6 y603 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x63 h5 y5ce ff6 fs1 fc0 sc0 ls0 ws0">c</div><div class="t m0 x19 h5 y15d ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 x1c h3 y69 ff3 fs0 fc0 sc0 ls0 ws0">G<span class="ff2">(</span>x<span class="ff2">)<span class="_ _6"> </span></span>dF<span class="_ _6"> </span><span class="ff2">(</span>x<span class="ff2">)</span>.</div><div class="t m0 xef h3 y61b ff2 fs0 fc0 sc0 ls0 ws0">If the in<span class="_ _5"></span>tegrals inv<span class="_ _5"></span>olv<span class="_ _5"></span>ed exist</div><div class="t m0 x5a h6 y160 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x5b h5 y449 ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 x159 h5 y3bc ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 xe h6 y61c ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x15b h3 y527 ff3 fs0 fc0 sc0 ls0 ws0">G<span class="ff2">(</span>x<span class="ff2 ls9">)+</span>H<span class="_ _15"></span><span class="ff2">(</span>x<span class="ff2">)</span></div><div class="t m0 xcc h6 y61c ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x6b h3 y527 ff3 fs0 fc0 sc0 ls0 ws0">dF<span class="_ _6"> </span><span class="ff2">(</span>x<span class="ff2 ls1">)=</span></div><div class="t m0 x17b h6 y160 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x186 h5 y449 ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 x163 h5 y3bc ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 x17d h3 y527 ff3 fs0 fc0 sc0 ls0 ws0">G<span class="ff2">(</span>x<span class="ff2">)<span class="_ _6"> </span></span>dF<span class="_ _6"> </span><span class="ff2">(</span>x<span class="ff2 ls9">)+</span></div><div class="t m0 x64 h6 y160 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xbc h5 y449 ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 x1e h5 y3bc ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 x37 h3 y527 ff3 fs0 fc0 sc0 ls0 ws0">H<span class="_ _2"></span><span class="ff2">(<span class="_ _5"></span><span class="ff3">x<span class="ff2">)<span class="_ _8"> </span></span>dF<span class="_ _2"></span><span class="ff2">(</span>x<span class="ff2">)</span>,</span></span></div><div class="t m0 x5a h6 y16a ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x5b h5 ya7 ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 x159 h5 y61d ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 xe h3 ya9 ff3 fs0 fc0 sc0 ls0 ws0">G<span class="ff2">(</span>x<span class="ff2">)<span class="_ _6"> </span></span>d</div><div class="t m0 x10e h6 y61e ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x69 h3 ya9 ff3 fs0 fc0 sc0 ls0 ws0">F<span class="_ _6"> </span><span class="ff2">(</span>x<span class="ff2 ls2">)+</span>H<span class="_ _15"></span><span class="ff2">(</span>x<span class="ff2">)</span></div><div class="t m0 x122 h6 y61e ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x31 h3 ya9 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x17b h6 y16a ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x186 h5 ya7 ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 x163 h5 y61d ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 x17d h3 ya9 ff3 fs0 fc0 sc0 ls0 ws0">G<span class="ff2">(</span>x<span class="ff2">)<span class="_ _6"> </span></span>dF<span class="_ _6"> </span><span class="ff2">(</span>x<span class="ff2 ls9">)+</span></div><div class="t m0 x64 h6 y16a ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xbc h5 ya7 ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 x1e h5 y61d ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 x37 h3 ya9 ff3 fs0 fc0 sc0 ls0 ws0">G<span class="ff2">(</span>x<span class="ff2">)<span class="_ _6"> </span></span>dH<span class="_ _2"></span><span class="ff2">(</span>x<span class="ff2">)</span>,</div><div class="t m0 x47 h6 y61f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x2a h5 y620 ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 x14e h5 y8e ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 x126 h4 y416 ff3 fs0 fc0 sc0 ls0 ws0">c<span class="_ _8"> </span><span class="ff4">·<span class="_ _8"> </span></span>G<span class="ff2">(</span>x<span class="ff2">)<span class="_ _6"> </span></span>dF<span class="_ _6"> </span><span class="ff2">(</span>x<span class="ff2 ls1">)=</span></div><div class="t m0 x4a h6 y621 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x13a h5 y620 ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 xce h5 y8e ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 x1b7 h3 y416 ff3 fs0 fc0 sc0 ls0 ws0">G<span class="ff2">(</span>x<span class="ff2">)<span class="_ _6"> </span></span>d</div><div class="t m0 x112 h6 y3c4 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x11d h4 y416 ff3 fs0 fc0 sc0 ls0 ws0">c<span class="_ _8"> </span><span class="ff4">·<span class="_ _8"> </span></span>F<span class="_ _6"> </span><span class="ff2">(</span>x<span class="ff2">)</span></div><div class="t m0 x62 h6 y3c4 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x36 h3 y416 ff2 fs0 fc0 sc0 ls0 ws0">=<span class="_ _7"> </span><span class="ff3">c</span></div><div class="t m0 x1d h6 y621 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xbc h5 y620 ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 x54 h5 y8e ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 x168 h3 y416 ff3 fs0 fc0 sc0 ls0 ws0">G<span class="ff2">(</span>x<span class="ff2">)<span class="_ _6"> </span></span>dF<span class="_ _6"> </span><span class="ff2">(</span>x<span class="ff2">)</span>,</div><div class="t m0 x14e h6 y479 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x126 h5 y270 ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 x156 h5 y47b ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 x9e h4 y622 ff3 fs0 fc0 sc0 ls0 ws0">G<span class="ff2">(</span>x<span class="ff2">)<span class="_ _6"> </span></span>dF<span class="_ _6"> </span><span class="ff2">(</span>x<span class="ff2 ls1">)=</span>G<span class="ff2">(</span>b<span class="ff2">)</span>F<span class="_ _6"> </span><span class="ff2">(</span>b<span class="ff2">)<span class="_ _8"> </span><span class="ff4">−<span class="_ _8"> </span></span></span>G<span class="ff2">(</span>a<span class="ff2">)</span>F<span class="_ _6"> </span><span class="ff2">(</span>a<span class="ff2">)<span class="_ _8"> </span><span class="ff4">−</span></span></div><div class="t m0 xbb h6 y479 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x54 h5 y270 ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 x1d h5 y47b ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 xbc h3 y622 ff3 fs0 fc0 sc0 ls0 ws0">F<span class="_ _6"> </span><span class="ff2">(</span>x<span class="ff2">)<span class="_ _6"> </span></span>dG<span class="ff2">(</span>x<span class="ff2">)</span>.</div><div class="t m0 xef h3 y2d0 ff2 fs0 fc0 sc0 ls0 ws0">If<span class="_ _7"> </span>the<span class="_ _8"> </span>integrals<span class="_ _8"> </span>inv<span class="_ _5"></span>olv<span class="_ _5"></span>ed<span class="_ _7"> </span>exist,<span class="_ _7"> </span>and<span class="_ _8"> </span><span class="ff3">F<span class="_ _0"> </span></span>p<span class="_ _3"></span>ossesses<span class="_ _7"> </span>a<span class="_ _8"> </span>deriv<span class="_ _5"></span>ativ<span class="_ _5"></span>e<span class="_ _7"> </span><span class="ff3">F</span></div><div class="t m0 x167 h5 y623 ff8 fs1 fc0 sc0 ls0 ws0"></div><div class="t m0 xba h3 y2d0 ff2 fs0 fc0 sc0 ls0 ws0">at<span class="_ _7"> </span>ev<span class="_ _5"></span>ery</div><div class="t m0 xef h3 y208 ff2 fs0 fc0 sc0 ls0 ws0">p<span class="_ _3"></span>oin<span class="_ _5"></span>t in [<span class="ff3">a,<span class="_ _8"> </span>b<span class="_ _5"></span><span class="ff2">] then</span></span></div><div class="t m0 x10 h6 yb6 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x1b5 h5 ya0 ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 xae h5 y3cc ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 x5d h3 y17f ff3 fs0 fc0 sc0 ls0 ws0">G<span class="ff2">(</span>x<span class="ff2">)<span class="_ _6"> </span></span>dF<span class="_ _6"> </span><span class="ff2">(</span>x<span class="ff2 lsf">)=</span></div><div class="t m0 x4d h6 yb6 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x13b h5 ya0 ff6 fs1 fc0 sc0 ls0 ws0">b</div><div class="t m0 x11d h5 y3cc ff6 fs1 fc0 sc0 ls0 ws0">a</div><div class="t m0 x7b h3 y17f ff3 fs0 fc0 sc0 ls0 ws0">G<span class="ff2">(</span>x<span class="ff2">)</span>F</div><div class="t m0 x1b h5 y9e ff8 fs1 fc0 sc0 ls0 ws0"></div><div class="t m0 x19 h3 y17f ff2 fs0 fc0 sc0 ls0 ws0">(<span class="ff3">x</span>)<span class="_ _6"> </span><span class="ff3">dx.</span></div><div class="t m0 x116 h3 y297 ff2 fs0 fc0 sc0 ls0 ws0">Cramer’s Rule</div><div class="t m0 x72 h5 y299 ff5 fs1 fc0 sc0 ls0 ws0">00<span class="_ _11"> </span>47<span class="_ _11"> </span>18<span class="_ _1e"> </span>76<span class="_ _11"> </span>29<span class="_ _11"> </span>93<span class="_ _11"> </span>85<span class="_ _11"> </span>34<span class="_ _1e"> </span>61<span class="_ _11"> </span>52</div><div class="t m0 x72 h5 y2d8 ff5 fs1 fc0 sc0 ls0 ws0">86<span class="_ _11"> </span>11<span class="_ _11"> </span>57<span class="_ _1e"> </span>28<span class="_ _11"> </span>70<span class="_ _11"> </span>39<span class="_ _11"> </span>94<span class="_ _11"> </span>45<span class="_ _1e"> </span>02<span class="_ _11"> </span>63</div><div class="t m0 x72 h5 y213 ff5 fs1 fc0 sc0 ls0 ws0">95<span class="_ _11"> </span>80<span class="_ _11"> </span>22<span class="_ _1e"> </span>67<span class="_ _11"> </span>38<span class="_ _11"> </span>71<span class="_ _11"> </span>49<span class="_ _11"> </span>56<span class="_ _1e"> </span>13<span class="_ _11"> </span>04</div><div class="t m0 x72 h5 y18d ff5 fs1 fc0 sc0 ls0 ws0">59<span class="_ _11"> </span>96<span class="_ _11"> </span>81<span class="_ _1e"> </span>33<span class="_ _11"> </span>07<span class="_ _11"> </span>48<span class="_ _11"> </span>72<span class="_ _11"> </span>60<span class="_ _1e"> </span>24<span class="_ _11"> </span>15</div><div class="t m0 x72 h5 y18e ff5 fs1 fc0 sc0 ls0 ws0">73<span class="_ _11"> </span>69<span class="_ _11"> </span>90<span class="_ _1e"> </span>82<span class="_ _11"> </span>44<span class="_ _11"> </span>17<span class="_ _11"> </span>58<span class="_ _11"> </span>01<span class="_ _1e"> </span>35<span class="_ _11"> </span>26</div><div class="t m0 x72 h5 y2a3 ff5 fs1 fc0 sc0 ls0 ws0">68<span class="_ _11"> </span>74<span class="_ _11"> </span>09<span class="_ _1e"> </span>91<span class="_ _11"> </span>83<span class="_ _11"> </span>55<span class="_ _11"> </span>27<span class="_ _11"> </span>12<span class="_ _1e"> </span>46<span class="_ _11"> </span>30</div><div class="t m0 x72 h5 y2a9 ff5 fs1 fc0 sc0 ls0 ws0">37<span class="_ _11"> </span>08<span class="_ _11"> </span>75<span class="_ _1e"> </span>19<span class="_ _11"> </span>92<span class="_ _11"> </span>84<span class="_ _11"> </span>66<span class="_ _11"> </span>23<span class="_ _1e"> </span>50<span class="_ _11"> </span>41</div><div class="t m0 x72 h5 y489 ff5 fs1 fc0 sc0 ls0 ws0">14<span class="_ _11"> </span>25<span class="_ _11"> </span>36<span class="_ _1e"> </span>40<span class="_ _11"> </span>51<span class="_ _11"> </span>62<span class="_ _11"> </span>03<span class="_ _11"> </span>77<span class="_ _1e"> </span>88<span class="_ _11"> </span>99</div><div class="t m0 x72 h5 y624 ff5 fs1 fc0 sc0 ls0 ws0">21<span class="_ _11"> </span>32<span class="_ _11"> </span>43<span class="_ _1e"> </span>54<span class="_ _11"> </span>65<span class="_ _11"> </span>06<span class="_ _11"> </span>10<span class="_ _11"> </span>89<span class="_ _1e"> </span>97<span class="_ _11"> </span>78</div><div class="t m0 x72 h5 y3d6 ff5 fs1 fc0 sc0 ls0 ws0">42<span class="_ _11"> </span>53<span class="_ _11"> </span>64<span class="_ _1e"> </span>05<span class="_ _11"> </span>16<span class="_ _11"> </span>20<span class="_ _11"> </span>31<span class="_ _11"> </span>98<span class="_ _1e"> </span>79<span class="_ _11"> </span>87</div><div class="t m0 x35 h3 y297 ff2 fs0 fc0 sc0 ls0 ws0">Fib<span class="_ _3"></span>onacci Num<span class="_ _5"></span>b<span class="_ _3"></span>ers</div><div class="t m0 x81 h3 y2ea ff2 fs0 fc0 sc0 ls0 ws0">If w<span class="_ _5"></span>e hav<span class="_ _5"></span>e equations:</div><div class="t m0 xc8 h3 y1d8 ff3 fs0 fc0 sc0 ls0 ws0">a</div><div class="t m0 x12f h5 y188 ff5 fs1 fc0 sc0 ls0 ws0">1<span class="ff6">,</span>1</div><div class="t m0 x143 h3 y1d8 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x107 h5 y188 ff5 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m0 x141 h3 y1d8 ff2 fs0 fc0 sc0 ls0 ws0">+<span class="_ _8"> </span><span class="ff3">a</span></div><div class="t m0 x149 h5 y188 ff5 fs1 fc0 sc0 ls0 ws0">1<span class="ff6">,</span>2</div><div class="t m0 x13e h3 y1d8 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x10a h5 y188 ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x10b h4 y1d8 ff2 fs0 fc0 sc0 ls0 ws0">+<span class="_ _8"> </span><span class="ff4 ls4">···<span class="_ _15"></span></span>+<span class="_ _8"> </span><span class="ff3">a</span></div><div class="t m0 x129 h5 y188 ff5 fs1 fc0 sc0 ls0 ws0">1<span class="ff6">,n</span></div><div class="t m0 x89 h3 y1d8 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x12a h5 y188 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 xc3 h3 y1d8 ff2 fs0 fc0 sc0 ls0 ws0">=<span class="_ _7"> </span><span class="ff3">b</span></div><div class="t m0 x171 h5 y188 ff5 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m0 xc8 h3 y625 ff3 fs0 fc0 sc0 ls0 ws0">a</div><div class="t m0 x12f h5 y18d ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">,</span>1</div><div class="t m0 x143 h3 y625 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x107 h5 y18d ff5 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m0 x141 h3 y625 ff2 fs0 fc0 sc0 ls0 ws0">+<span class="_ _8"> </span><span class="ff3">a</span></div><div class="t m0 x149 h5 y18d ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">,</span>2</div><div class="t m0 x13e h3 y625 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x10a h5 y18d ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x10b h4 y625 ff2 fs0 fc0 sc0 ls0 ws0">+<span class="_ _8"> </span><span class="ff4 ls4">···<span class="_ _15"></span></span>+<span class="_ _8"> </span><span class="ff3">a</span></div><div class="t m0 x129 h5 y18d ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">,n</span></div><div class="t m0 x89 h3 y625 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x12a h5 y18d ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 xc3 h3 y625 ff2 fs0 fc0 sc0 ls0 ws0">=<span class="_ _7"> </span><span class="ff3">b</span></div><div class="t m0 x171 h5 y18d ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x143 h3 y316 ff2 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x143 h3 y1da ff2 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x143 h3 y571 ff2 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x10a h3 y316 ff2 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x10a h3 y1da ff2 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x10a h3 y571 ff2 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x4 h3 y316 ff2 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x4 h3 y1da ff2 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x4 h3 y571 ff2 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 xc8 h3 y566 ff3 fs0 fc0 sc0 ls0 ws0">a</div><div class="t m0 xe2 h5 y198 ff6 fs1 fc0 sc0 ls0 ws0">n,<span class="ff5">1</span></div><div class="t m0 x143 h3 y566 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x107 h5 y198 ff5 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m0 x141 h3 y566 ff2 fs0 fc0 sc0 ls0 ws0">+<span class="_ _8"> </span><span class="ff3">a</span></div><div class="t m0 x149 h5 y198 ff6 fs1 fc0 sc0 ls0 ws0">n,<span class="ff5">2</span></div><div class="t m0 x8b h3 y566 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x102 h5 y198 ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 x1ac h4 y566 ff2 fs0 fc0 sc0 ls0 ws0">+<span class="_ _8"> </span><span class="ff4 ls4">···<span class="_ _15"></span></span>+<span class="_ _8"> </span><span class="ff3">a</span></div><div class="t m0 x190 h5 y198 ff6 fs1 fc0 sc0 ls0 ws0">n,n</div><div class="t m0 xd8 h3 y566 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 xd9 h5 y198 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 xc9 h3 y566 ff2 fs0 fc0 sc0 ls0 ws0">=<span class="_ _7"> </span><span class="ff3">b</span></div><div class="t m0 x1b3 h5 y198 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x81 h3 y4db ff2 fs0 fc0 sc0 ls0 ws0">Let<span class="_ _7"> </span><span class="ff3">A<span class="_ _7"> </span></span><span class="ls1">=(<span class="_ _b"></span><span class="ff3 ls0">a</span></span></div><div class="t m0 x93 h5 y199 ff6 fs1 fc0 sc0 ls0 ws0">i,j</div><div class="t m0 x143 h3 y4db ff2 fs0 fc0 sc0 ls0 ws0">)<span class="_ _7"> </span>and<span class="_ _7"> </span><span class="ff3">B<span class="_ _7"> </span></span>b<span class="_ _3"></span>e<span class="_ _7"> </span>the<span class="_ _7"> </span>column<span class="_ _8"> </span>matrix<span class="_ _7"> </span>(<span class="ff3">b</span></div><div class="t m0 xcb h5 y199 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x136 h3 y4db ff2 fs0 fc0 sc0 ls0 ws0">).<span class="_ _34"> </span>Then</div><div class="t m0 x81 h4 y218 ff2 fs0 fc0 sc0 ls0 ws0">there<span class="_ _0"> </span>is a<span class="_ _0"> </span>unique<span class="_ _0"> </span>solution<span class="_ _0"> </span>iff det<span class="_ _8"> </span><span class="ff3">A<span class="_ _7"> </span><span class="ff4"></span></span>= 0.<span class="_ _11"> </span>Let<span class="_ _0"> </span><span class="ff3">A</span></div><div class="t m0 x14f h5 y19a ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 xdc h3 y218 ff2 fs0 fc0 sc0 ls10 ws0">be <span class="ff3 ls0">A</span></div><div class="t m0 x81 h3 y569 ff2 fs0 fc0 sc0 ls0 ws0">with column <span class="ff3">i </span>replaced by <span class="ff3">B<span class="_ _3"></span></span>.<span class="_ _34"> </span>Then</div><div class="t m0 xf4 h3 y626 ff3 fs0 fc0 sc0 ls0 ws0">x</div><div class="t m0 x8b h5 ye8 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x102 h3 y627 ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 xf5 h3 y2e3 ff2 fs0 fc0 sc0 ls0 ws0">det<span class="_ _6"> </span><span class="ff3">A</span></div><div class="t m0 xd7 h5 yea ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x124 h3 y628 ff2 fs0 fc0 sc0 ls0 ws0">det<span class="_ _6"> </span><span class="ff3">A</span></div><div class="t m0 x125 h3 y629 ff3 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x6d h3 y62a ff2 fs0 fc0 sc0 ls0 ws0">1<span class="ff3">,<span class="_ _6"> </span></span>1<span class="ff3">,<span class="_ _8"> </span></span>2<span class="_ _5"></span><span class="ff3">,<span class="_ _6"> </span><span class="ff2">3</span>,<span class="_ _8"> </span><span class="ff2">5<span class="_ _5"></span><span class="ff3">,<span class="_ _6"> </span><span class="ff2">8</span>,<span class="_ _8"> </span><span class="ff2">13<span class="_ _5"></span><span class="ff3">,<span class="_ _6"> </span><span class="ff2">21</span>,<span class="_ _8"> </span><span class="ff2">34<span class="_ _5"></span><span class="ff3">,<span class="_ _6"> </span><span class="ff2">55</span>,<span class="_ _6"> </span><span class="ff2">89</span><span class="ls4">,...</span></span></span></span></span></span></span></span></div><div class="t m0 x6d h3 y62b ff2 fs0 fc0 sc0 ls0 ws0">Definitions:</div><div class="t m0 x6d h3 y62c ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 x13b h5 y62d ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x7b h3 y62e ff2 fs0 fc0 sc0 ls0 ws0">=<span class="_ _7"> </span><span class="ff3">F</span></div><div class="t m0 x6e h5 y62d ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff8">−<span class="ff5">1</span></span></div><div class="t m0 x1cc h3 y62e ff2 fs0 fc0 sc0 ls0 ws0">+<span class="ff3">F</span></div><div class="t m0 xb1 h5 y62d ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff8">−<span class="ff5">2</span></span></div><div class="t m0 xd0 h3 y62e ff3 fs0 fc0 sc0 ls3 ws0">,F</div><div class="t m0 x7e h5 y62d ff5 fs1 fc0 sc0 ls0 ws0">0</div><div class="t m0 x23 h3 y62e ff2 fs0 fc0 sc0 ls0 ws0">=<span class="_ _7"> </span><span class="ff3">F</span></div><div class="t m0 x183 h5 y62d ff5 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m0 x38 h3 y62e ff2 fs0 fc0 sc0 ls1 ws0">=1<span class="_ _b"></span><span class="ff3 ls0">,</span></div><div class="t m0 x4f h3 y62f ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 x62 h5 y3d2 ff8 fs1 fc0 sc0 ls0 ws0">−<span class="ff6">i</span></div><div class="t m0 x63 h4 y630 ff2 fs0 fc0 sc0 ls1 ws0">=(<span class="_ _b"></span><span class="ff4 ls0">−<span class="ff2">1)</span></span></div><div class="t m0 x1f h5 y631 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff8">−<span class="ff5">1</span></span></div><div class="t m0 x7e h3 y630 ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 x23 h5 y3d2 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x7d h3 y630 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x18 h3 y37d ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 x6e h5 y195 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 xb8 h3 y37d ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x52 h5 y5e1 ff5 fs1 fc0 sc0 ls0 ws0">1</div><div class="t m0 x63 h5 y31b ff8 fs1 fc0 sc0 ls0 ws0">√</div><div class="t m0 x1c h5 y632 ff5 fs1 fc0 sc0 ls0 ws0">5</div><div class="t m0 x1a8 h6 yd3 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x166 h3 y37d ff3 fs0 fc0 sc0 ls0 ws0">φ</div><div class="t m0 x168 h5 yd1 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 xdf h4 y37d ff4 fs0 fc0 sc0 ls0 ws0">−</div><div class="t m0 xbd h3 y565 ff2 fs0 fc0 sc0 ls0 ws0">ˆ</div><div class="t m0 x65 h3 y37d ff3 fs0 fc0 sc0 ls0 ws0">φ</div><div class="t m0 x66 h5 yd1 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x23 h6 yd3 ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xbf h3 y37d ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x6d h3 y21a ff2 fs0 fc0 sc0 ls0 ws0">Cassini’s iden<span class="_ _5"></span>tity:<span class="_ _34"> </span>for <span class="ff3 ls1">i&gt;</span>0:</div><div class="t m0 x7a h3 y633 ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 x169 h5 y1e3 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">+1</span></div><div class="t m0 x62 h3 y634 ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 x1b h5 y1e3 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff8">−<span class="ff5">1</span></span></div><div class="t m0 xb1 h4 y634 ff4 fs0 fc0 sc0 ls0 ws0">−<span class="_ _8"> </span><span class="ff3">F</span></div><div class="t m0 x168 h5 y3d6 ff5 fs1 fc0 sc0 ls0 ws0">2</div><div class="t m0 xa3 h5 y2ae ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x7c h4 y634 ff2 fs0 fc0 sc0 ls1 ws0">=(<span class="_ _b"></span><span class="ff4 ls0">−<span class="ff2">1)</span></span></div><div class="t m0 xd2 h5 y3d6 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 xc0 h3 y634 ff3 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x6d h3 yea ff2 fs0 fc0 sc0 ls0 ws0">Additiv<span class="_ _5"></span>e rule:</div><div class="t m0 xb6 h3 y2bb ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 x7a h5 y635 ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff5">+</span>k</div><div class="t m0 x113 h3 y2bb ff2 fs0 fc0 sc0 ls0 ws0">=<span class="_ _7"> </span><span class="ff3">F</span></div><div class="t m0 xde h5 y635 ff6 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x1c h3 y2bb ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 xb9 h5 y635 ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff5">+1</span></div><div class="t m0 xdf h3 y2bb ff2 fs0 fc0 sc0 ls0 ws0">+<span class="_ _8"> </span><span class="ff3">F</span></div><div class="t m0 x66 h5 y635 ff6 fs1 fc0 sc0 ls0 ws0">k<span class="ff8">−<span class="ff5">1</span></span></div><div class="t m0 xba h3 y2bb ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 xc0 h5 y635 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x38 h3 y2bb ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x4e h3 y636 ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 x187 h5 y22a ff5 fs1 fc0 sc0 ls0 ws0">2<span class="ff6">n</span></div><div class="t m0 x6e h3 y637 ff2 fs0 fc0 sc0 ls0 ws0">=<span class="_ _7"> </span><span class="ff3">F</span></div><div class="t m0 x51 h5 y22a ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x52 h3 y637 ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 x1b2 h5 y22a ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff5">+1</span></div><div class="t m0 x37 h3 y637 ff2 fs0 fc0 sc0 ls0 ws0">+<span class="_ _8"> </span><span class="ff3">F</span></div><div class="t m0 x7e h5 y22a ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff8">−<span class="ff5">1</span></span></div><div class="t m0 x1a7 h3 y637 ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 x165 h5 y22a ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x22 h3 y637 ff3 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x6d h3 y638 ff2 fs0 fc0 sc0 ls0 ws0">Calculation by matrices:</div><div class="t m0 x6d h6 y19f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 xfb h3 y639 ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 xa1 h5 y63a ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff8">−<span class="ff5">2</span></span></div><div class="t m0 x17a h3 y63b ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 x63 h5 y63a ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff8">−<span class="ff5">1</span></span></div><div class="t m0 xfb h3 y63c ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 xa1 h5 y63d ff6 fs1 fc0 sc0 ls0 ws0">n<span class="ff8">−<span class="ff5">1</span></span></div><div class="t m0 x51 h3 y63c ff3 fs0 fc0 sc0 ls0 ws0">F</div><div class="t m0 x180 h5 y63d ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 xcf h6 y19f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x37 h3 y63e ff2 fs0 fc0 sc0 ls0 ws0">=</div><div class="t m0 x55 h6 y19f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x66 h3 y63b ff2 fs0 fc0 sc0 ls5 ws0">01</div><div class="t m0 x66 h3 y63c ff2 fs0 fc0 sc0 ls5 ws0">11</div><div class="t m0 xc0 h6 y19f ff7 fs0 fc0 sc0 ls0 ws0"></div><div class="t m0 x19b h5 y108 ff6 fs1 fc0 sc0 ls0 ws0">n</div><div class="t m0 x39 h3 y63f ff3 fs0 fc0 sc0 ls0 ws0">.</div><div class="t m0 x18a h3 y1e4 ff2 fs0 fc0 sc0 ls0 ws0">The<span class="_ _7"> </span>Fib<span class="_ _3"></span>onacci<span class="_ _7"> </span>num<span class="_ _5"></span>ber<span class="_ _7"> </span>system:</div><div class="t m0 x18a h3 y640 ff2 fs0 fc0 sc0 ls0 ws0">Ev<span class="_ _5"></span>ery<span class="_ _1e"> </span>in<span class="_ _5"></span>teger<span class="_ _1e"> </span><span class="ff3">n<span class="_ _1e"> </span></span>has<span class="_ _1e"> </span>a<span class="_ _1e"> </span>unique</div><div class="t m0 x18a h3 y641 ff2 fs0 fc0 sc0 ls0 ws0">represen<span class="_ _5"></span>tation</div><div class="t m0 x29 h3 y4e9 ff3 fs0 fc0 sc0 ls0 ws0">n<span class="_ _7"> </span><span class="ff2">=<span class="_ _7"> </span></span>F</div><div class="t m0 xff h5 y642 ff6 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x15b h7 y643 ffc fs2 fc0 sc0 ls0 ws0">1</div><div class="t m0 x5c h3 y4e9 ff2 fs0 fc0 sc0 ls0 ws0">+<span class="_ _8"> </span><span class="ff3">F</span></div><div class="t m0 x10e h5 y642 ff6 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x69 h7 y643 ffc fs2 fc0 sc0 ls0 ws0">2</div><div class="t m0 x3d h4 y4e9 ff2 fs0 fc0 sc0 ls0 ws0">+<span class="_ _8"> </span><span class="ff4 ls4">···<span class="_ _15"></span></span>+<span class="_ _8"> </span><span class="ff3">F</span></div><div class="t m0 x40 h5 y642 ff6 fs1 fc0 sc0 ls0 ws0">k</div><div class="t m0 x1cd h7 y643 ffa fs2 fc0 sc0 ls0 ws0">m</div><div class="t m0 x42 h3 y4e9 ff3 fs0 fc0 sc0 ls0 ws0">,</div><div class="t m0 x18a h3 y10c ff2 fs0 fc0 sc0 ls0 ws0">where<span class="_ _34"> </span><span class="ff3">k</span></div><div class="t m0 x126 h5 y644 ff6 fs1 fc0 sc0 ls0 ws0">i</div><div class="t m0 x15f h4 y10c ff4 fs0 fc0 sc0 ls0 ws0">≥<span class="_ _34"> </span><span class="ff3">k</span></div><div class="t m0 x10e h5 y644 ff6 fs1 fc0 sc0 ls0 ws0">i<span class="ff5">+1</span></div><div class="t m0 x138 h3 y10c ff2 fs0 fc0 sc0 ls0 ws0">+<span class="_ _7"> </span>2<span class="_ _34"> </span>for<span class="_ _1e"> </span>all<span class="_ _0"> </span><span class="ff3">i</span>,</div><div class="t m0 x18a h4 y4f4 ff2 fs0 fc0 sc0 ls0 ws0">1<span class="_ _7"> </span><span class="ff4">≤<span class="_ _7"> </span><span class="ff3 ls1">i&lt;m<span class="_ _15"></span></span></span>and <span class="ff3">k</span></div><div class="t m0 x3d h5 y1eb ff6 fs1 fc0 sc0 ls0 ws0">m</div><div class="t m0 x2e h4 y4f4 ff4 fs0 fc0 sc0 ls0 ws0">≥<span class="_ _7"> </span><span class="ff2">2.</span></div><div class="t m0 x81 h3 y645 ff2 fs0 fc0 sc0 ls0 ws0">Impro<span class="_ _5"></span>vemen<span class="_ _5"></span>t<span class="_ _12"> </span>mak<span class="_ _5"></span>es<span class="_ _12"> </span>strait<span class="_ _12"> </span>roads,<span class="_ _36"> </span>but<span class="_ _12"> </span>the<span class="_ _12"> </span>crooked</div><div class="t m0 x81 h3 y3e1 ff2 fs0 fc0 sc0 ls0 ws0">roads without Improv<span class="_ _5"></span>emen<span class="_ _5"></span>t, are roads of Genius.</div><div class="t m0 x81 h3 y2bd ff2 fs0 fc0 sc0 ls0 ws0">– William Blake (The Marriage of Hea<span class="_ _5"></span>v<span class="_ _5"></span>en and Hell)</div></div><div class="pi" data-data='{"ctm":[1.673203,0.000000,0.000000,1.673203,0.000000,0.000000]}'></div></div></div>
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