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Math Help - Fibonacci sequence proof

  1. #1
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    Fibonacci sequence proof

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    \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!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by wik_chick88 View Post
    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
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  3. #3
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    it just became a whole lot easier!! thankyou!
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