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SOLVED: Recall that the Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, and is defined recursively as f1 = 1, f2 = 1, and fn = fn-1 fn-2 for n ≥ 3, where fn denotes the nth term of the sequence.(a) Prove by induction that for positive integers n, f1 f2 .. fn = fn 2 - 1.(b) Prove by induction that for integers n > 3, f2 1 f2 3f3-1 2(f2-2 f2-3 .. f2 f1) = fn 2.(c) Prove by induction that for positive integers n, f2 2f4 3f6 .. nf2n = nf2n 1 - f2n.(d) Prove by induction tha
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