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Math Help - proving a sequence

  1. #1
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    proving a sequence

    Im having some trouble figuring this out.. could someone help me out a bit?

    Define the sequence of F as follows
    F1=1, F2=1, Fn=Fn-1+Fn-2 n>=3

    prove F1^2+F2^2+...Fn^2=FnFn+1 while n is a positive integer
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  2. #2
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    Quote Originally Posted by JoeBabble View Post
    Im having some trouble figuring this out.. could someone help me out a bit?

    Define the sequence of F as follows
    F1=1, F2=1, Fn=Fn-1+Fn-2 n>=3

    prove F1^2+F2^2+...Fn^2=FnFn+1 while n is a positive integer
    That is, of course, the Fibonacci series. The problem you have is that you are trying to prove something that isn't true! Have you tried proving this by induction? When n= 1, this says F1^2+ F2^2= 1+ 1= 2= F2F3= 1*2= 2.
    If it is true that F_1^2+ ...+ F_k^2= F_kF_{k+1}, for some k, then F_1^2+ ...+ F_k^2+ F_{k+1}^2= F_kF_{k+1}+ F_{k+1}^2.
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