Unformatted text preview: Prove, using strong induction, that g(n) > 4 n , for all n>1. 9) The Fibonacci numbers are defined as follows: F 1 = F 2 = 1, and F n = F n-1 + F n-2 , for all integers n > 2. Prove the following closed summation closed form using induction: ∑ = n i i F 1 2 = F n F n+1 , for integers n > 0. 10) Let g: A → A be a bijection. For n ≥ 2, define g n = g ° g ° ... ° g, where g is composed with itself n times. Prove that for n ≥ 2, that g n is a bijection from A to A as well, and show that (g n )-1 = (g-1 ) n . (Here you may assume that the composition of two bijections is also a bijection.)...
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- Fall '09
- Natural number, Euclidean algorithm