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Fibonacci numbers

  1. May 17, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove that f_2n+1=(f_n+1)^2+(f_n)^2​


    2. Relevant equations

    (f_n)^2=(f_2n)-2(f_n-1)(f_n)

    3. The attempt at a solution

    i started with plugging in for the formula in (f_n)^2 and doing the same for (f_n+1)^2

    but im not sure if i'm even going in the right direction

    i got to the point (f_2n+1) = f_2n+2 + f_2n -2f_n(f_n+1 + f_n-1)
     
  2. jcsd
  3. May 17, 2010 #2

    lanedance

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    Homework Helper

    how about using induction... (not that i've tried yet, but worth a shot)
     
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