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5. Show that 1.2+2·3+3.4+...+ (n − 1)(n) = (n³ − n)

5. Show that 1.2+2·3+3.4+...+ (n − 1)(n) = (n³ − 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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5. Show that \(1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + (n - 1)(n) = \frac{1}{3}(n^3 - n)\).
Transcribed Image Text:5. Show that \(1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + \ldots + (n - 1)(n) = \frac{1}{3}(n^3 - n)\).
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