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간단한 요약

http://bomber0.byus.net/mimetex/mimetex.cgi?

• [1]http://bomber0.byus.net/mimetex/mimetex.cgi?F(n+2)=F(n+1)+F(n)
• \(F(n+2)=F(n+1)+F(n)\)

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

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• http://bomber0.byus.net/mimetex/mimetex.cgi?\varphi = \frac{1 + \sqrt{5}}{2} \approx 1.61803\,39887\dots\
• \(\varphi = \frac{1 + \sqrt{5}}{2} \approx 1.6180339887\cdots\)
• [2]http://bomber0.byus.net/mimetex/mimetex.cgi?\lim_{n\to\infty}\frac{F(n+1)}{F(n)}=\varphi
• \(\lim_{n\to\infty}\frac{F(n+1)}{F(n)}=\varphi\)
•  
  http://bomber0.byus.net/mimetex/mimetex.cgi? (-1)^{n} = F_{n+1}F_{n-1} - F_n^2\
  
• \( F_{n+1}F_{n-1} - F_n^2=(-1)^{n}\)
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  http://bomber0.byus.net/mimetex/mimetex.cgi?\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
  
• \(\sum_{n=1}^{\infty}\frac{(-1)^{n+1}}{F_nF_{n+1}}=\sum_n^{\infty}{\frac{F_{n}}{F_{n+1}}-\frac{F_{n-1}}{F_{n}}}=\varphi -1\)
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  http://bomber0.byus.net/mimetex/mimetex.cgi? \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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