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(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
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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#6 part c

### 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
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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