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Prove the statement using induction. 1² +22+3² +4² + ... + n² = If n € N, then If n ≤ N, then ++ +· n(n+1)(2n+1) 6 1.2+2·3+3.4+4.5++ n(n + 1) = n(n+1)(n+2) for every positive integer n. n (n+1)! 1. (n+1)!*

Prove the statement using induction. 1² +22+3² +4² + ... + n² = If n € N, then If n ≤ N, then ++ +· n(n+1)(2n+1) 6 1.2+2·3+3.4+4.5++ n(n + 1) = n(n+1)(n+2) for every positive integer n. n (n+1)! 1. (n+1)!*

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.5: Mathematical Induction
Problem 32E: Prove by induction that 1+2n3n for n1.
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Prove the statement using induction. 12 +22² +3² +4²+...+n² = n(n+1)(2n+1) 6 for every positive integer n. If n € N, then 1-2 +2·3+3.4+4.5+ ... + n(n+1) = n(n+1)(n+2)¸ 3 If ne N, then ++ + n (n+1)! 1 (n+1)!*
Transcribed Image Text:Prove the statement using induction. 12 +22² +3² +4²+...+n² = n(n+1)(2n+1) 6 for every positive integer n. If n € N, then 1-2 +2·3+3.4+4.5+ ... + n(n+1) = n(n+1)(n+2)¸ 3 If ne N, then ++ + n (n+1)! 1 (n+1)!*
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