Unformatted text preview: n > 4n for all integers n ≥ 0. 6. Let b 1 =3, b 2 =5 and b k =3b k-1- 2b k-2 for all k>2. Prove by induction that b n = 2 n +1 for all integers n ≥ 1. 7. Suppose we have N deck chairs on board the Titanic and it ʼ s our job to stack them all together into one pile. We can take any pile (of one or more chairs) and place it on top of another pile to create a new pile. Assuming none of the chairs is initially stacked on any other, how many steps (a step is the act of creating one new pile out of two) does it take us to stack all N chairs? Give a proof using strong induction. Then go hop in a lifeboat. 8. Prove using induction that the following statement holds for all n ≥ 0: if n is odd then 9 n mod 10 = 9 and if n is even then 9 n mod 10 = 1. COMP SCI 360 Assignment #5 Penn State University Fall 2010 PAGE 1 OF 1...
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- Fall '08
- Addition, Summation, Natural number, Penn State University