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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
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