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Þrove that for all positive integers n, 1° + 2° + 3° + . + n° = (ma+)". a. Show it is true for n= 1. Show your work here: b. Assume it is true for n= k. Show your work here: c. Prove it is true for k + 1. Show your work here:

Þrove that for all positive integers n, 1° + 2° + 3° + . + n° = (ma+)". a. Show it is true for n= 1. Show your work here: b. Assume it is true for n= k. Show your work here: c. Prove it is true for k + 1. Show your work here:

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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**20. Prove that for all positive integers \( n \), the equation \( 1^3 + 2^3 + 3^3 + \ldots + n^3 = \left(\frac{n(n+1)}{2}\right)^2 \) holds.** a. **Show it is true for \( n = 1 \):** *Show your work here:* --- b. **Assume it is true for \( n = k \):** *Show your work here:* --- c. **Prove it is true for \( k + 1 \):** *Show your work here:* ---
Transcribed Image Text:**20. Prove that for all positive integers \( n \), the equation \( 1^3 + 2^3 + 3^3 + \ldots + n^3 = \left(\frac{n(n+1)}{2}\right)^2 \) holds.** a. **Show it is true for \( n = 1 \):** *Show your work here:* --- b. **Assume it is true for \( n = k \):** *Show your work here:* --- c. **Prove it is true for \( k + 1 \):** *Show your work here:* ---
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