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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Transcribed Image Text: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.
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