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Prove Fibonacci formula with induction?

  1. Sep 27, 2009 #1
    1. The problem statement, all variables and given/known data

    I'm trying to prove the Fibonacci formula with induction, but I'm having difficulties. This is what I'm trying to prove:

    http://www.psc-consulting.ca/fenske/cpjav17e.gif [Broken]

    2. Relevant equations



    3. The attempt at a solution

    So I did a base case, n=1. It worked, so move to induction. Now, I have absolutely *no* idea how to get this to work, even start? So I took it and added n+1 to both sides. Then what? I tried multiplying by sqrt(5) to make it a lil simpler (dunno if i'm allowed to do that) but I'm really not sure where to go next. Any help would be very much appreciated.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 28, 2009 #2
    Try to assume that the formula is true for f(n) and for f(n-1).

    what base case(s) do you have to prove?
     
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