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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 n1 + F n2 , 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 = (g1 ) n . (Here you may assume that the composition of two bijections is also a bijection.)...
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This document was uploaded on 06/09/2011.
 Fall '09

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