# Fibonacci

• Jan 25th 2009, 02:17 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:
$f_n=\frac{1}{\sqrt 5}\left(\left(\frac{1+\sqrt 5}{2}\right)^{n}-\left(\frac{1-\sqrt 5}{2}\right)^{n}\right)$

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

• Jan 25th 2009, 02:31 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:
$f_n=\frac{1}{\sqrt 5}\left(\left(\frac{1+\sqrt 5}{2}\right)^{n}-\left(\frac{1-\sqrt 5}{2}\right)^{n}\right)$

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