Proof of F^2_n + F^2_(n+1) = F_(2n+1) for n>=1

[StellaLuna]

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?

 

[kate1729]

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.