(i) Convergent (j) Convergent (k) Convergent (1) Divergent 6. Determine whether the series is absolutely convergent, conditionally converge Give reasons for your answer. (a) (b) (-1)" √n (-1)-In n³+1 2n (Ⓒ) [(-1)"In 2(-1)³¹ (211) n=1 ANSWERS. (a) Conditionally convergent (b) Absolutely convergent
(i) Convergent (j) Convergent (k) Convergent (1) Divergent 6. Determine whether the series is absolutely convergent, conditionally converge Give reasons for your answer. (a) (b) (-1)" √n (-1)-In n³+1 2n (Ⓒ) [(-1)"In 2(-1)³¹ (211) n=1 ANSWERS. (a) Conditionally convergent (b) Absolutely convergent
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
#6 part c

Transcribed Image Text:### Series Convergence Worksheet
#### 5. Determine the Convergence or Divergence of the Following Series
For each series, determine whether it converges or diverges. The options are: Divergent, Convergent.
(a) \(\sum_{n=1}^{\infty} \frac{2n-1}{n^3 + n}\)
(b) \(\sum_{n=1}^{\infty} \frac{2n+1}{n^2 + n}\)
(c) \(\sum_{n=1}^{\infty} \frac{n!}{(2n)!}\)
(d) \(\sum_{n=1}^{\infty} \frac{4^n}{n!}\)
(e) \(\sum_{n=1}^{\infty} \frac{n}{3^n}\)
(f) \(\sum_{n=1}^{\infty} \frac{n}{(\ln n)^n}\)
(g) \(\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{n^2 + 1}\)
(h) \(\sum_{n=2}^{\infty} \frac{(-1)^n}{n-1}\)
#### Answers:
(a) Divergent
(b) Divergent
(c) Convergent
(d) Convergent
(e) Convergent
(f) Divergent
(g) Convergent
(h) Convergent
(i) Convergent
(j) Convergent
(k) Convergent
(l) Divergent
#### 6. Determine Whether the Series is Absolutely Convergent, Conditionally Convergent, or Divergent
Determine the nature of convergence of each series. Provide reasons for your answer.
(a) \(\sum_{n=1}^{\infty} \frac{(-1)^n}{\sqrt{n}}\)
(b) \(\sum_{n=1}^{\infty} \frac{(-1)^{n-1} \ln n}{n^3 + 1}\)
(c) \(\sum_{n=1}^{\infty} (-1)^n \ln\left(\frac{2n}{n+1}\right)\)
#### Answers:
(a) Conditionally convergent
(b) Absolutely convergent
(c) Divergent
This material provides
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