1 1 Let P(n) be the statement that 1-2 +·..+ 2-3 n(n+1) n for n > 1. What is the best inductive n+1 hypothesis? Assume for an arbitrary fixed integer k 1, 1-2 k(k+1) 2-3 k+1 Assume P(k) : 2 +23 ++ for some integer k. k+1 k(k+1) Assume for an arbitrary fixed integer k > 1, +23++ k+1Yk+21 k+1 k+2 1-2 2-3 Assume P(k): for any integer k. k+1 k(k+1) Assume P(k): for any integer k>1. 1-2 2-3 k(k+1) k+1

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