Verify the following identity for Fibonacci numbers 
This is a homework problem that I would very much appreciate some help with. Thanks!

One could proceed by inductin as follows:
For $n=0$, both sides are $1$. For $n=1$, both sides are $2$.
Suppose now that it holds for $n=k\ge 1$. Then $\sum_{i=0}^{k+1}F_i^2=F_kF_{k+1}+F_{k+1}^{2}=F_{k+1}(F_k+F_{k+1})=F_{k+1}F_{k+2}$. 
