# Fibonacci

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• Jan 25th 2009, 01:17 PM
javax
Fibonacci
Hello everybody. I need some help onn the problems. I always had problem with these:

i). Prove that the n-th term of Fibonacci numbers is given with this formula:
$\displaystyle f_n=\frac{1}{\sqrt 5}\left(\left(\frac{1+\sqrt 5}{2}\right)^{n}-\left(\frac{1-\sqrt 5}{2}\right)^{n}\right)$

ii). Let it be $\displaystyle F_n=2^{2^{n}}+1$. Prove that $\displaystyle F_0 F_1 F_2 \cdots F_{n-1}=F_n - 2, n>0$

I appreciate your help.
• Jan 25th 2009, 01:31 PM
Shyam
Quote:

Originally Posted by javax
Hello everybody. I need some help onn the problems. I always had problem with these:

i). Prove that the n-th term of Fibonacci numbers is given with this formula:
$\displaystyle f_n=\frac{1}{\sqrt 5}\left(\left(\frac{1+\sqrt 5}{2}\right)^{n}-\left(\frac{1-\sqrt 5}{2}\right)^{n}\right)$

ii). Let it be $\displaystyle F_n=2^{2^{n}}+1$. Prove that $\displaystyle F_0 F_1 F_2 \cdots F_{n-1}=F_n - 2, n>0$

I appreciate your help.

Please see

Fibonacci number - Wikipedia, the free encyclopedia