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Fibonacci Numbers

  1. Mar 7, 2010 #1
    Could anyone help me with the following proof?

    F^2_n + F^2_(n+1) = F_(2n+1) for ngreater than or equal to 1?
  2. jcsd
  3. Mar 9, 2010 #2
    I think a good technique would be to use induction (I don't know if it actually works, I haven't done the proof).

    You first consider a base case, in this case it would be n = 1. Check to see that for this the formula works.

    Then comes the inductive step. Assume that this formula works for n =k, and then prove that it works for n = k+1.

    Then you're done. The reason this proof works is that truth for n=1 implies truth for n=2, and then n=3, and so on infinitely, so the formula would work for all n.
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