this is wrong. you haven't verified the statement holds for the base case

Hint: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?

(and in general, you get the next Fibonacci number by adding the previous two, this will come in handy)