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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