26. Which of the following infinite series con- verges conditionally? 1. Σ (-1)* k=1 2 Σ α 3. Σ n=1 4. m = 1 5. 4 8k ln(k) + 6 8 6m – 4 6(-n)" (n + 5)n Σ cos(nn) n=1 Σ(1) Τ 5η 8η + 4 n

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
26.
Which of the following infinite series con-
verges conditionally?
1. Σ (-1)*
k=1
2.
3.
4.
5.
IM8 M8 IM M8
Σ
m=1
8
6m
4
8k: ln(k) + 6
4
6(-n)"
(n + 5)n
cos(nn)
Π
Σ (3)
5η
8η + 4
n
Transcribed Image Text:26. Which of the following infinite series con- verges conditionally? 1. Σ (-1)* k=1 2. 3. 4. 5. IM8 M8 IM M8 Σ m=1 8 6m 4 8k: ln(k) + 6 4 6(-n)" (n + 5)n cos(nn) Π Σ (3) 5η 8η + 4 n
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Follow-up Question
**Question 26: Which of the following infinite series converges conditionally?**

1. \(\sum_{k=1}^{\infty} \frac{(-1)^k \cdot 4}{8k \ln(k) + 6}\)

2. \(\sum_{m=1}^{\infty} \frac{8}{6m - 4}\)

3. \(\sum_{n=1}^{\infty} \frac{6(-n)^n}{(n+5)^n}\)

4. \(\sum_{n=1}^{\infty} \cos(n\pi) \left(\frac{5n}{8n+4}\right)^n\)

5. \(\sum_{n=1}^{\infty} \left(-\frac{3}{2}\right)^n\)
Transcribed Image Text:**Question 26: Which of the following infinite series converges conditionally?** 1. \(\sum_{k=1}^{\infty} \frac{(-1)^k \cdot 4}{8k \ln(k) + 6}\) 2. \(\sum_{m=1}^{\infty} \frac{8}{6m - 4}\) 3. \(\sum_{n=1}^{\infty} \frac{6(-n)^n}{(n+5)^n}\) 4. \(\sum_{n=1}^{\infty} \cos(n\pi) \left(\frac{5n}{8n+4}\right)^n\) 5. \(\sum_{n=1}^{\infty} \left(-\frac{3}{2}\right)^n\)
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