# Math Help - Fibonacci sequence proof

1. ## 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!

2. 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

3. it just became a whole lot easier!! thankyou!