Q1: Consider the Fibonacci sequence f1, f2, f3,··· defined recursively by f₁ = 1, f2 = 1, and fn = fn-1 + fn-2 for all n

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Q1 Consider The Fibonacci Sequence F1 F2 F3 Defined Recursively By F 1 F2 1 And Fn Fn 1 Fn 2 For All N 1 (29.31 KiB) Viewed 29 times

Q1: Consider the Fibonacci sequence f1, f2, f3,··· defined recursively by f₁ = 1, f2 = 1, and fn = fn-1 + fn-2 for all n ≥ 3. [5] (a) Prove that fn ≤ (13/8)" for all n ≥ 1. [4] (b) Prove that f2 + f4 + · ... + f2n = f2n+1 - 1 for all n > 1.