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Math Help - proof involving Fibonacci sequence

  1. #1
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    Exclamation proof involving Fibonacci sequence

    The fibonacci sequence, F(n) is defined:
    F(n) = F(n-1) + F(n-2) for each n = 2,3,... with F(0)=1 and F(1)=1.

    Use strong induction to prove that

    F(n) = [PHI^(n+1)-(-PHI)^(-n-1)] / (sqrt(5)) for each integer n greater than or equal to 0.
    Where PHI=(1+sqrt(5))/2

    Please help!!
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  2. #2
    Super Member TheChaz's Avatar
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    Re: proof involving Fibonacci sequence

    This is exactly the same problem as was asked and answered last weekend, elsewhere...
    Prove this formula for the Fibonacci Sequence - Mathematics - Stack Exchange
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