I am confused about mathematical and strong induction about the Fibonacci numbers. I wrote some Basis Steps, but I am not sure how to prove it in the inductive step. Could you help me?

Thanks,

8. Let P (n) be the statement Fi = Fn+2 - 1 Basis Step: When n = 1, F; - 1 = 9. Let P (n) be the statement Fn. We need to show that P (n) is true whatever n is an integer greater than or equal to 1. Basis Step: When n = 1, -*(25)= When n = 2, * (5) =1 P (1 ) and P (2) are true. Inductive Step: Assume that P (k) is true. We need to show that P (k + 1) is true.For the next 3 questions, we will use Fibonacci Numbers. Fibonacci Numbers is defined as a sequence F, with F1 = 1, F2 = 1, Fm = Fo-1 + Fn-2(for all n > 3). 8. (10pts) Use Mathematical Induction to prove that _F; = En+2-1, for every integer n >1. 9. (10pts) Use Strong Induction to prove that for every integer n 2 1, 1 Fn = 1+ v5, 1 - v5 2 2 )"]