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Thread: Fibonacci

  1. December 4th 2008, 04:26 PM #1
    mathman88
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    Fibonacci

    I've been stuck on this one for quite some time now and would really appreciate a little hint.

    Let F_i be the i^{th} Fibonacci number.

    Show that F_{2n} = F_{n+1}^2+F_{n-1}^2
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  2. December 4th 2008, 05:20 PM #2
    galactus
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    I believe that identity is F_{2n}=F^{2}_{n+1}-F^{2}_{n-1}

    You have a plus. Perhaps that is why you are having trouble.

    F_{n+1}^{2}-F_{n-1}^{2}=\left(F_{n+1}-F_{n-1}\right)\left(F_{n+1}+F_{n-1}\right)
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  3. December 4th 2008, 06:04 PM #3
    mathman88
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    whoops, thats what I meant, where do I go from here?
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