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Math Help - Real Analysis: Fibonacci Numbers

  1. #1
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    Real Analysis: Fibonacci Numbers

    Here is the problem:



    Need help please!!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Phyxius117 View Post
    Here is the problem:



    Need help please!!
    I will give you a push.

    I leave the base case to you.

    For our inductive step, assume that F_iF_{i - 2} = (F_{i - 1})^2 + (-1)^i (1).

    We show that F_{i + 1}F_{i - 1} = (F_i)^2 + (-1)^{i + 1}.

    Note that

    F_{i + 1}F_{i - 1} = (F_i + F_{i - 1})F_{i - 1}

    = F_i F_{i - 1} + (F_{i - 1})^2

    Now, change (F_{i - 1})^2 using the equation in (1) and simplify to get the desired result.

    Try it
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  3. #3
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    ty so much!! will try it!
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