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b 2x 1! + 5x 2! + .+ (nt + 1)п! %3D п(п + 1)! + 10 x 3! + .. 2 3 + .. 1 n 1 + + + = 1 - 2! 3! 4! (п + 1)! (п + 1)!

b 2x 1! + 5x 2! + .+ (nt + 1)п! %3D п(п + 1)! + 10 x 3! + .. 2 3 + .. 1 n 1 + + + = 1 - 2! 3! 4! (п + 1)! (п + 1)!

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter13: Sequences And Series
Section13.CT: Chapter Test
Problem 10CT
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5 Prove by mathematical induction that for all positive integer values of n: (п + 1)! — 1 b 2 x 1! + 5 × 2! + 10 × 3! + ·.. + (n² + 1)n! = n(n + 1)! 1 x 1! + 2 × 2! + 3 × 3! + · ·. + n × n! = (n + 1)! - 1 1 C 2! 2 3 + + :.: + 4! n 1 = 1 (п + 1)! ... 3! (n + 1)!
Transcribed Image Text:5 Prove by mathematical induction that for all positive integer values of n: (п + 1)! — 1 b 2 x 1! + 5 × 2! + 10 × 3! + ·.. + (n² + 1)n! = n(n + 1)! 1 x 1! + 2 × 2! + 3 × 3! + · ·. + n × n! = (n + 1)! - 1 1 C 2! 2 3 + + :.: + 4! n 1 = 1 (п + 1)! ... 3! (n + 1)!
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