Fun with Algorithms. Recall that Fibonacci numbers form a sequence Fn where Fo = 0, Fi = 1, and Fn-1 + Fn-2. The standard algorithm for finding the n-th Fibonacci number takes O(n) time. The goal of this question is to design a significantly faster algorithm for this problem. (+10 points) (a) Prove by induction that for all n > 1: [Fn+1 [1] d)* = [ FR Fn-1 Fn (b) Use the first part to design an algorithm that finds Fn in O(log n) time