1. Fibonacci

I've been stuck on this one for quite some time now and would really appreciate a little hint.

Let $F_i$ be the $i^{th}$ Fibonacci number.

Show that $F_{2n} = F_{n+1}^2+F_{n-1}^2$

2. I believe that identity is $F_{2n}=F^{2}_{n+1}-F^{2}_{n-1}$

You have a plus. Perhaps that is why you are having trouble.

$F_{n+1}^{2}-F_{n-1}^{2}=\left(F_{n+1}-F_{n-1}\right)\left(F_{n+1}+F_{n-1}\right)$

3. whoops, thats what I meant, where do I go from here?