피보나치 수열

F₀	F₁	F₂	F₃	F₄	F₅	F₆	F₇	F₈	F₉	F₁₀	F₁₁	F₁₂	F₁₃	F₁₄	F₁₅	F₁₆	F₁₇	F₁₈	F₁₉	F₂₀
0	1	1	2	3	5	8	13	21	34	55	89	144	233	377	610	987	1597	2584	4181	6765

http://bomber0.byus.net/mimetex/mimetex.cgi?F(n+2)=F(n+1)+F(n)
\(\varphi = \frac{1 + \sqrt{5}}{2} \approx 1.61803\,39887\dots\,\)
\[\lim_{n\to\infty}\frac{F(n+1)}{F(n)}=\varphi,\]
\((-1)^{n} = F_{n+1}F_{n-1} - F_n^2\,.\)
\Sigma_{n=1}^{\infty}\frac{(-1)^{n+1}}{F_nF_{n+1}}=\Sigma_n^{\infty}\frac{F_{n}}{F_{n+1}}-\frac{F_{n-1}}{F_{n}}}=\varphi -1
\Prod_{n=2}^{\infty}(1+\frac{(-1)^{n}}{F_n^2})=\Prod_{n=2}^{\infty}\frac{F_n^2+(-1)^n}{F_n^2}=\Prod_{n=2}^{\infty}\frac{F_{n-1}F_{n+1}}{F_n^2}=\varphi

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