Discrete and Foundational Mathematics I quiz 7 Solutions

Now consider the rst k people in line the rst of

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Unformatted text preview: a man. (b) Case II: The penultimate person is a man. Now consider the first k people in line. The first of these is a woman and the last of these is the penultimate man. According to the induction hypothesis, somewhere in this line of k people we have a woman directly in front of a man. QED 3) Prove: 1− 1 2 1− 1 4 1− 1 8 ··· 1 − 1 2n ≥ 1 1 + 4 2n+1 for all positive integers n. Proof by induction on n: 1. Base case: Prove true for n = 1. LHS = 1 − So LHS ≥ RHS. Done with base case. 1 2 1 = 2 . RHS...
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