Q: Show that the Fibonacci numbers F(1),F(2),F(3),... ,where F(1)= F(2)=1 and F(k)= F(k-2) + F(k-1) for k>2 satisfy the following equality for all n (greater or equal to) 1.
(F(1))^2 + (F(2))^2 + (F(3))^2+.....+ (F(n))^2 = F(n) * F(n+1)
I did the basis step:
1^2 + 1^2 = 1
but how do I do the inductive step for this question?
Thanks,
Creative