The Fibonacci numbers F0, F1, F2,..., are defined by the rule
F0 = 0, F1 = 1, Fn = Fn-1 + Fn-2.
In this problem we will confirm that this sequence grows exponentially fast and obtain some bounds on its growth.
(a) Use induction to prove that Fn ≥ 20.5n for n ≥ 6.
(b) Find a constant c < 1 such that Fn < 2cn for all n ≥ 0. Show that your answer is correct.
(c) What is the largest c you can find for which Fn = Ω(2cn)?
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