Combinatorics proof involving Fibonacci numbers [duplicate]

I've found an interesting problem in my Combinatorics class notes but I am unsure how to start or even where to start. The question is:

Prove that $$\sum_{j=1}^nf_j^2$$ = $$f_nf_{n+1}$$, where $$f_j$$ are Fibonacci numbers.

Would anyone mind giving me a hint or at least giving me a start?

assume this is true for some $$m$$. So
$$\Sigma_{j=1}^{m} f_j^2= f_mf_{m+1}$$.Now for $$m+1$$, we can write
$$\Sigma_{j=1}^{m+1} f_j^2=\Sigma_{j=1}^{m} f_j^2+ f^2_{m+1}= f_mf_{m+1} + f^2_{m+1} = f_{m+1}(f_m+f_{m+1}) =f_{m+1}f_{m+2}$$.
So by proof by induction it is true for $$n= 2$$ ($$1^2+1^2+2^2=2*3$$) let us say. and if it is true for $$m$$ then true for $$m+1$$. Since it is true for n=2, it is true for all natural numbers >=2. Hence the proof