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Suppose you want to show that 1 2+2 3+3.4+ 4.5+ ... + n(n+1) = n(n+1)(n+2) 3 is true for all positive integers n. In a proof by mathematical induction of this formula, the statement Sk or P (k) in the inductive hypothesis is which of the following statements?

Suppose you want to show that 1 2+2 3+3.4+ 4.5+ ... + n(n+1) = n(n+1)(n+2) 3 is true for all positive integers n. In a proof by mathematical induction of this formula, the statement Sk or P (k) in the inductive hypothesis is which of the following statements?

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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Suppose you want to show that 1 2+2 3+3.4+ 4.5+ ... + n(n+1) n(n+1)(n+2) 3 is true for all positive integers n. In a proof by mathematical induction of this formula, the statement Skor P (k) in the inductive hypothesis is which of the following statements? 1 2+2 3+3.4+ 4.5+ k(k+1)(k+2) ... + k (k+1) 3 1 2+2 3+3.4+ 4.5++ k (k+1) (k+1)((k+1)+1)((k+1)+2) 3 = = 1.2 +2.3 + 3.4 + 4.5+ ··· + (k+ 1) ((k+1) + 1) (k+1)((k+1)+1)((k+1)+2) = 3 01.2+2.3 + 3.4 + 4.5++ (k+1) ((k+1) +1) k(k+1)(k+2) 3
Transcribed Image Text:Suppose you want to show that 1 2+2 3+3.4+ 4.5+ ... + n(n+1) n(n+1)(n+2) 3 is true for all positive integers n. In a proof by mathematical induction of this formula, the statement Skor P (k) in the inductive hypothesis is which of the following statements? 1 2+2 3+3.4+ 4.5+ k(k+1)(k+2) ... + k (k+1) 3 1 2+2 3+3.4+ 4.5++ k (k+1) (k+1)((k+1)+1)((k+1)+2) 3 = = 1.2 +2.3 + 3.4 + 4.5+ ··· + (k+ 1) ((k+1) + 1) (k+1)((k+1)+1)((k+1)+2) = 3 01.2+2.3 + 3.4 + 4.5++ (k+1) ((k+1) +1) k(k+1)(k+2) 3
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