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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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1 Let P(n) be the statement that 1-2 1 +· ·+ =- for n > 1. What is the best inductive n+1 2-3 n(n+1) hypothesis? 1 Assume for an arbitrary fixed integer k 2 1, + +···+ 2-3 k(k+1) k+1 k for some integer k. k+1 1 1 Assume P(k): +23 +· · · + %3D 2-3 k(k+1) k+1 Assume for an arbitrary fixed integer k > 1, +…+ 2-3 (k+1)(k+2) 1-2 k+2 Assume P(k) : for any integer k. k(k+1) k+1 1 +·.+ 2-3 for any integer k 1. k+1 1 Assume P(k) : + k(k+1) 1-2
Transcribed Image Text:1 Let P(n) be the statement that 1-2 1 +· ·+ =- for n > 1. What is the best inductive n+1 2-3 n(n+1) hypothesis? 1 Assume for an arbitrary fixed integer k 2 1, + +···+ 2-3 k(k+1) k+1 k for some integer k. k+1 1 1 Assume P(k): +23 +· · · + %3D 2-3 k(k+1) k+1 Assume for an arbitrary fixed integer k > 1, +…+ 2-3 (k+1)(k+2) 1-2 k+2 Assume P(k) : for any integer k. k(k+1) k+1 1 +·.+ 2-3 for any integer k 1. k+1 1 Assume P(k) : + k(k+1) 1-2
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