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Math Help - Fibonacci Sequence - Induction Proof

  1. #1
    WWU
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    Fibonacci Sequence - Induction Proof

    Hello,

    I am having problems with writing an inductive proof for the following problem:


    => Prove by induction that F(n+k) = F(k)F(n+1) + F(k-1)F(n)


    Now I know that my basis is: F(0) = 0 and F(1) = 1

    I am having trouble even getting started or figuring out where to start, any tips would be much appreciated!
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  2. #2
    MHF Contributor
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    Quote Originally Posted by WWU View Post
    Hello,

    I am having problems with writing an inductive proof for the following problem:


    => Prove by induction that F(n+k) = F(k)F(n+1) + F(k-1)F(n)


    Now I know that my basis is: F(0) = 0 and F(1) = 1

    I am having trouble even getting started or figuring out where to start, any tips would be much appreciated!
    With induction, you let n\leq k where k is an arbitary integer.

    Assume P(k) is true and prove P(k+1) is true.
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  3. #3
    MHF Contributor chiph588@'s Avatar
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    Quote Originally Posted by WWU View Post
    Hello,

    I am having problems with writing an inductive proof for the following problem:


    => Prove by induction that F(n+k) = F(k)F(n+1) + F(k-1)F(n)


    Now I know that my basis is: F(0) = 0 and F(1) = 1

    I am having trouble even getting started or figuring out where to start, any tips would be much appreciated!
    You should fix  k and induct on  n , treating  k as a constant.

    Your base case is  F(k) = F(k)F(1)+F(k-1)F(0) .
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