1. Prove that for any natural n the following holds 1.2+2.3+...+ (n – 1) · n = (п — 1)п(п + 1) 3 2. Prove that for any natural n the following holds п (2n – 1)(2n + 1) 2n +1 1.3 3.5

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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How to prove these two questions?

1. Prove that for any natural n the following holds
1.2+2.3+...+ (n – 1) · n =
(п — 1)п(п + 1)
3
2. Prove that for any natural n the following holds
п
(2n – 1)(2n + 1)
2n +1
1.3
3.5
Transcribed Image Text:1. Prove that for any natural n the following holds 1.2+2.3+...+ (n – 1) · n = (п — 1)п(п + 1) 3 2. Prove that for any natural n the following holds п (2n – 1)(2n + 1) 2n +1 1.3 3.5
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