5. (Scheinerman, Exercise 21.7:) Suppose Fn denotes the nth Fibonacci num- ber, where Fo= 1, F₁ = 1, Fn = Fn-1 + Fn-2 for n ≥ 2. The inequality Fn > 1.6" is true for all n that are large enough. Do some calculations to find out for what values of n this inequality holds. Then, prove your assertion using contradiction and smallest counterexample. (Note: you want to prove a statement of the form: "For all integers n ≥ N, Fn> 1.6" Your task is to first figure out what number N should be.) Hint: N= 29.

5. (Scheinerman, Exercise 21.7:) Suppose Fn denotes the nth Fibonacci num- ber, where Fo= 1, F₁ = 1, Fn = Fn-1 + Fn-2 for n ≥ 2. The inequality Fn > 1.6" is true for all n that are large enough. Do some calculations to find out for what values of n this inequality holds. Then, prove your assertion using contradiction and smallest counterexample. (Note: you want to prove a statement of the form: "For all integers n ≥ N, Fn> 1.6" Your task is to first figure out what number N should be.) Hint: N= 29.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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