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)!*
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.4: Mathematical Induction
Problem 26E
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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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