Proving the Induction Step for a Fibonacci Property

[dlemke]

For all k \in N, f(2k + 1)= f^{2}(k) + f^{2}(k + 1)

I couldn't find this one in the forum... I am stuck on the induction step, really I have no idea how to get it going. Oh, and the k statements should be in subscript, I was having real problems with LaTex, misreading subs and sups. Thanks for any help, it is greatly, greatly appreciated.

 

[fzero]

Start from the definition of the sequence

f_{2k+3} = f_{2k+2} + f_{2k-1}.

For odd indices, use the formula to be proven. For the even index, find a way to rewrite the term as a sum of odd index objects.

 

[dlemke]

<br /> f_{2k+3} = f_{2k+2} + f_{2k-1}.<br />

Oh, nice, so you are taking the LHS and rewriting it, and hopefully eventually transforming it into the original RHS of the assumption. Thank you so much! That first step just kills me. Ok, I will work more on this in the morning and repost. Thank you for taking the time to help.