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Math Help - Sum of first n fibbonaci numbers

  1. #1
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    Sum of first n fibbonaci numbers

    Hey, I was just wondering if there was an explicit expression for the sum of the first n fibbonaci numbers.
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  2. #2
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by Chris11 View Post
    Hey, I was just wondering if there was an explicit expression for the sum of the first n fibbonaci numbers.
     \sum_{i=1}^n F_i = F_{n+2}-1

    This can be shown by induction or by the explicit formula for the Fibonacci sequence.
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    Thanks.
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    MHF Contributor Also sprach Zarathustra's Avatar
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    Proof:


    F_1=F_3-F_2
    F_2=F_4-F_3
    F_3=F_5-F_4
    .
    .
    .
    F_{n-1}=F_{n+1}-F{n}
    F_n=F_{n+2}-F_{n+1}

    now add them... what you get?
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