The inequality F n 1.6 n is true for all n that are large enough. Do some calculations to find out for what values of n this inequality holds.

The inequality Fn > 1.6n 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 > 1.6n.” Your task is to first figure out what number N should be.)

Given Fn 1.6n Let W x N:Fn 1.6n F0 1.60 1n 1, F1 1 1.61n2Fn Fn 2 Fn 1 1.6 n 2 1.6n 1 1.6 n 2 2.6 1.6 n 2 2.56 1.6 n 2 1.6 2 1.6 nSo the statement is true for x n and contradicting n W