Question: Fun with Algorithms. Recall that Fibonacci numbers form a sequence Fn where F0=0,F1=1, and Fn=Fn1+Fn2. The standard algorithm for finding the n-th Fibonacci number takes

Fun with Algorithms. Recall that Fibonacci numbers form a sequence Fn

Fun with Algorithms. Recall that Fibonacci numbers form a sequence Fn where F0=0,F1=1, and Fn=Fn1+Fn2. 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 n1 : [1110]n=[Fn+1FnFnFn1]. (b) Use the first part to design an algorithm that finds Fn in O(logn) time

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