Thread: Prove Conjecture

Prove conjecture for the sum of the squares of the first n Fibonacci numbers

(F1) ^2 + (F2) ^ 2 .... + (Fn) ^2

Thanks for the help!!

What is the conjecture?

well I'm really trying to prove

f1^2 + F2^2 +.... Fn^2 = (Fn) (Fn+1) by assuming n = K + 1

Thanks for Speedy response

This is certainly an inductive proof. But it is not difficult.

We have:







So it looks like the first few cases are true.

Suppose is true.

Then .

And the induction is complete.

ahh thanks for the help