# Fibonacci sequence proof

• Apr 4th 2011, 07:28 PM
wik_chick88
Fibonacci sequence proof
Show:
$\sum^{\infty}_{n=2} \frac{1}{f_{n-1}f_{n+1}} = 1$

i think we have to use the fact that
$\frac{1}{f_{n-1}f_{n+1}} = \frac{1}{f_{n-1}f_{n}} - \frac{1}{f_{n}f_{n+1}} (for \ n \geq 2)$

no idea where to start!
• Apr 4th 2011, 11:57 PM
CaptainBlack
Quote:

Originally Posted by wik_chick88
Show:
$\sum^{\infty}_{n=2} \frac{1}{f_{n-1}f_{n+1}} = 1$

i think we have to use the fact that
$\frac{1}{f_{n-1}f_{n+1}} = \frac{1}{f_{n-1}f_{n}} - \frac{1}{f_{n}f_{n+1}} (for \ n \geq 2)$

no idea where to start!

Two words: telescoping sum

CB
• Apr 5th 2011, 03:29 AM
wik_chick88
it just became a whole lot easier!! thankyou!