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For each integer n2 2, let P(n) be the following equation (n – 1)n(2n + 5) (i – 1)(i + 1) = 72 - 6 i=1 Note that the left had side of the equation is (i – 1)(i+1) = 0 - 2 + 1 -3+2·4+3-5+ ...+ (n – 1)(n + 1) . (a) Write P(2). Is P(2) true? (b) Use mathematical induction to prove that P(n) holds true for all integersn22.

For each integer n2 2, let P(n) be the following equation (n – 1)n(2n + 5) (i – 1)(i + 1) = 72 - 6 i=1 Note that the left had side of the equation is (i – 1)(i+1) = 0 - 2 + 1 -3+2·4+3-5+ ...+ (n – 1)(n + 1) . (a) Write P(2). Is P(2) true? (b) Use mathematical induction to prove that P(n) holds true for all integersn22.

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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For each integer n > 2, let P(n) be the following equation (n – 1)n(2n + 5) (i – 1)(i + 1) = 6. i=1 Note that the left had side of the equation is > (i – 1)(i+ 1) = 0 - 2 + 1 · 3 +2 · 4+3 · 5+ i=1 ...+ (n – 1)(n +1) . (a) Write P(2). Is P(2) true? (b) Use mathematical induction to prove that P(n) holds true for all integersn > 2.
Transcribed Image Text:For each integer n > 2, let P(n) be the following equation (n – 1)n(2n + 5) (i – 1)(i + 1) = 6. i=1 Note that the left had side of the equation is > (i – 1)(i+ 1) = 0 - 2 + 1 · 3 +2 · 4+3 · 5+ i=1 ...+ (n – 1)(n +1) . (a) Write P(2). Is P(2) true? (b) Use mathematical induction to prove that P(n) holds true for all integersn > 2.
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