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Prove the following equations by induction. In each case, n is a positive integer. a. 1+4+7++ (3n-2) = n(3n-1) 2 b. 1³ +2³++n²³ = n²(n+1)²

Prove the following equations by induction. In each case, n is a positive integer. a. 1+4+7++ (3n-2) = n(3n-1) 2 b. 1³ +2³++n²³ = n²(n+1)²

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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help with 22.4 (b) and then write answer in latex code

22.4. Prove the following equations by induction. In each case, \( n \) is a positive integer. a. \( 1 + 4 + 7 + \cdots + (3n - 2) = \frac{n(3n-1)}{2} \) b. \( 1^3 + 2^3 + \cdots + n^3 = \frac{n^2(n+1)^2}{4} \)
Transcribed Image Text:22.4. Prove the following equations by induction. In each case, \( n \) is a positive integer. a. \( 1 + 4 + 7 + \cdots + (3n - 2) = \frac{n(3n-1)}{2} \) b. \( 1^3 + 2^3 + \cdots + n^3 = \frac{n^2(n+1)^2}{4} \)
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