$\newcommand{\ds}{\displaystyle}$ $\newcommand{\ve}[1]{\overrightarrow{\mathbf{#1}}}$ $\newcommand{\ora}{\overrightarrow}$ $\newcommand{\com}[1]{\left\langle #1 \right\rangle}$ $\newcommand{\mb}{\mathbf}$ $\newcommand{\ivec}{\hat{\mbox{\bf{\dotlessi}}}}$ $\newcommand{\jvec}{\hat{\mbox{\bf{\dotlessj}}}}$ $\newcommand{\kvec}{\hat{\mbox{\bf{k}}}}$ $\newcommand{\magn}[1]{\left|\left| #1 \right|\right|}$

Series Convergence/Divergence

Click on each problem to expand and view the problem. You can then download a solution to the problem in PDF format. You can collapse the problem by clicking on the problem again.

• Exam 2, Spring 2006, Problem 6

• Exam 2, Fall 2009, Problem 6

• Exam 2, Spring 2010, Problem 5a

• Exam 2, Spring 2010, Problem 5b

• Exam 2, Spring 2012, Problem 5

Determine whether each of the following series converges or diverges. Indicate the method you are using.

(a) $\ds\sum_{k=1}^\infty\frac{k^2}{k^4+1}$

(b) $\ds\sum_{k=1}^\infty\frac{k!}{k^k}$

• Exam 2, Fall 2012, Problem 5

Determine whether or not the following infinite series converge. Justify your answers.

(a) $\ds\sum_{k=1}^\infty\frac{k-1}{k^3+5}$

(b) $\ds\sum_{k=3}^\infty\frac{1}{(\ln k)^{10}}$

• Exam 2, Spring 2013, Problem 3

Determine whether the following series converge or not.

(a) $\ds\sum_{n=1}^\infty\cos\left(\frac{1}{n}\right)$

(b) $\ds\sum_{n=1}^\infty\left(\frac{n}{5n+3}\right)^n$

(c) $\ds\sum_{n=1}^\infty\frac{\sin^2(n)}{n^2}$

• Exam 2, Study Guide 3, Problem 16

• Exam 2, Study Guide 3, Problem 17

• Exam 2, Study Guide 3, Problem 18

• Exam 2, Study Guide 3, Problem 19

• Exam 2, Study Guide 3, Problem 20

• Exam 2, Study Guide 3, Problem 21

• Exam 2, Study Guide 3, Problem 22

• Exam 2, Study Guide 3, Problem 23

• Exam 2, Study Guide 3, Problem 24

• Final Exam, Fall 2008, Problem 7

• Final Exam, Spring 2009, Problem 8

• Final Exam, Fall 2009, Problem 8

• Final Exam, Spring 2010, Problem 3

• Final Exam, Fall 2011, Problem 2

(a) $\ds \sum_{k=2}^\infty\frac{1}{k\ln(k)}$

(b) $\ds \sum_{k=1}^\infty\frac{(-1)^kk^2}{2^k}$

• Final Exam, Spring 2012, Problem 4

Determine whether each of the following series converges or diverges. Moreover, for those that converge, compute their sum. Indicate the method you are using.

(a) $\ds\sum_{n=1}^\infty\frac{-2}{n(n+1)}$

(b) $\ds\sum_{n=3}^\infty\frac{6}{\pi^n}$

(c) $\ds\sum_{k=2}^\infty\left(\frac{3k^3}{2k^3+9k^2+2k}\right)^{k/2}$

• Final Exam, Spring 2012, Problem 5

Determine whether the following series (a) converges absolutely, (b) converges conditionally, or (c) diverges. Justify your answer. $$\sum_{n=20}^\infty\frac{(-1)^n}{\ln(\ln n)}$$

• Final Exam, Study Guide, Problem 9

• Final Exam, Study Guide, Problem 10
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}