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Let P(n) be the statement 1² + 2² + ... + n² = for the positive integer n. What is the inductive step? O n(n+1) (2n+1) k(k+ 1) (2k + 1) 6 6

Let P(n) be the statement 1² + 2² + ... + n² = for the positive integer n. What is the inductive step? O n(n+1) (2n+1) k(k+ 1) (2k + 1) 6 6

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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Let P(n) be the statement 1² +2²+...+ n²: = for the positive integer n. What is the inductive step? O O k (k+ 1) (2k + 1) 6 n(n+1) (2n+1) 1² +2²+...+k² 1² +2²+ 1² +2²+ + (k+1) ² 1² +2²+ ... + k² = 6 ... + (k+ 1)² = k(k+ 1) (2k + 1) 6 (k+ 1) ( (k+1) + 1) (2(k+ 1) + 1) 6 (k+ 1) ((k+ 1) + 1) (2(k+1) + 1) 6
Transcribed Image Text:Let P(n) be the statement 1² +2²+...+ n²: = for the positive integer n. What is the inductive step? O O k (k+ 1) (2k + 1) 6 n(n+1) (2n+1) 1² +2²+...+k² 1² +2²+ 1² +2²+ + (k+1) ² 1² +2²+ ... + k² = 6 ... + (k+ 1)² = k(k+ 1) (2k + 1) 6 (k+ 1) ( (k+1) + 1) (2(k+ 1) + 1) 6 (k+ 1) ((k+ 1) + 1) (2(k+1) + 1) 6
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