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Question 1*. Prove, using mathematical induction, that n(3n 1) - 1 + 4 + 7 + ·.. + (3n – 5) + (3n – 2) - %3D for all positive integers n.

Question 1*. Prove, using mathematical induction, that n(3n 1) - 1 + 4 + 7 + ·.. + (3n – 5) + (3n – 2) - %3D for all positive integers n.

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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Question 1*. Prove, using mathematical induction, that n(3n – 1) 1 + 4 + 7 + ·.. + (3n – 5) + (3n – 2) = %D - for all positive integers n.
Transcribed Image Text:Question 1*. Prove, using mathematical induction, that n(3n – 1) 1 + 4 + 7 + ·.. + (3n – 5) + (3n – 2) = %D - for all positive integers n.
Question 2*. Prove, using mathematical induction, that 1 1 + 5 +... + 1 3 3 5 7 (2n – 1)(2n + 1) 2n + 1' for all positive integers n. Question 3*. Prove, using mathematical induction, that 8" 3"is divisible by 5 for all integers n 2 1. Question 4*. Prove, using mathematical induction, that 13 + 23 + 33 + .+n3 (n(n + 1))? 4 for all positive integers n. Question 5. Prove, using mathematical induction, that 1 1 +-+ 4 1 1 + 2n - 1 2(1 2n for all positive integers n.
Transcribed Image Text:Question 2*. Prove, using mathematical induction, that 1 1 + 5 +... + 1 3 3 5 7 (2n – 1)(2n + 1) 2n + 1' for all positive integers n. Question 3*. Prove, using mathematical induction, that 8" 3"is divisible by 5 for all integers n 2 1. Question 4*. Prove, using mathematical induction, that 13 + 23 + 33 + .+n3 (n(n + 1))? 4 for all positive integers n. Question 5. Prove, using mathematical induction, that 1 1 +-+ 4 1 1 + 2n - 1 2(1 2n for all positive integers n.
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