fn is the nth Fibonacci number

Prove that f1(^2)+f2(^2)+...+fn(^2)=fn fn+1 whenever n is a positive integer.

Here's what I have so far:

Let P(n) be f1(^2)+f2(^2)+...fn(^2)=fn fn+1

Basis step: P(1) is true since f1(2)=1=f2(^2)

Inductive Step: Assume P(n)) is true

Then f1(^2)+f2(^2)+...fn(^2)+fn+1(^2)=fn fn+1 + fn+1(^2)

Have I done this right so far, and if so, where do I go from here?