Question: Consider Fibonacci number F(N), where N is a positive integer, defined as follows. F(1) = 1 F(2) = 1 F(N) = F(N-1) + F(N-2) for

Consider Fibonacci number F(N), where N is a positive integer, defined as follows. F(1) = 1 F(2) = 1 F(N) = F(N-1) + F(N-2) for N > 2

a) Write a recursive function that computes Fibonacci number for a given integer N 1.

b) Prove the following theorem using induction: F(N) < N for integer N 1, where = (1+5)/2.

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