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$\displaystyle \sum^{\infty}_{n=2} \frac{1}{f_{n-1}f_{n+1}} = 1$

i think we have to use the fact that

$\displaystyle \frac{1}{f_{n-1}f_{n+1}} = \frac{1}{f_{n-1}f_{n}} - \frac{1}{f_{n}f_{n+1}} (for \ n \geq 2)$

no idea where to start!

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- Apr 4th 2011, 06:28 PMwik_chick88Fibonacci sequence proof
Show:

$\displaystyle \sum^{\infty}_{n=2} \frac{1}{f_{n-1}f_{n+1}} = 1$

i think we have to use the fact that

$\displaystyle \frac{1}{f_{n-1}f_{n+1}} = \frac{1}{f_{n-1}f_{n}} - \frac{1}{f_{n}f_{n+1}} (for \ n \geq 2)$

no idea where to start! - Apr 4th 2011, 10:57 PMCaptainBlack
- Apr 5th 2011, 02:29 AMwik_chick88
it just became a whole lot easier!! thankyou!