11n 10 Σ n2- 2n n 3

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

Does the series converge or diverge?

11n 10
Σ
n2- 2n
n 3
Transcribed Image Text:11n 10 Σ n2- 2n n 3
Expert Solution
Step 1

The given series,

11п - 10
п - 2n
п3
Step 2

The given series can be written as,

10
11п
1n10
п? — 2n
n-2n
n2-2n
п3
п3
11
10
-Σ
{ (п-2)п
п-2
п
11
1
1
- SΣ
(п-2) п
п-2
Σ
1
п- 2
-|S
8
8
Step 3

Using the p-series test such that,

Converges If p >1
Diverges ; If ps1
1
8
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