Intermediate Math Problem of the Week 10/5/2017

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  • Thread starter Thread starter PF PotW Robot
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SUMMARY

The discussion centers on evaluating the sum of the alternating series $$\sum\limits_{n = 1}^\infty \frac{(-1)^{n-1}}{n^4}$$. Participants are encouraged to explore various methods for solving this problem, with the potential for prizes for innovative approaches. Community engagement is emphasized, with members invited to check solutions and contribute alternative methods. The problem is presented as part of the Intermediate Math Problem of the Week series, hosted by Math Help Boards.

PREREQUISITES
  • Understanding of alternating series and convergence criteria
  • Familiarity with p-series and their properties
  • Basic knowledge of mathematical series and summation techniques
  • Experience with mathematical problem-solving and proof techniques
NEXT STEPS
  • Research the properties of alternating series and their convergence
  • Study the relationship between p-series and alternating p-series
  • Explore advanced summation techniques, such as Abel's or Dirichlet's tests
  • Investigate mathematical video resources that explain series evaluation methods
USEFUL FOR

Mathematics enthusiasts, educators, and students looking to deepen their understanding of series convergence and problem-solving strategies in advanced mathematics.

PF PotW Robot
Here is this week's intermediate math problem of the week. We have several members who will check solutions, but we also welcome the community in general to step in. We also encourage finding different methods to the solution. If one has been found, see if there is another way. Occasionally there will be prizes for extraordinary or clever methods. Spoiler tags are optional.

Evaluate the sum of the alternating series $$\sum\limits_{n = 1}^\infty \frac{(-1)^{n-1}}{n^4}$$

(PotW thanks to our friends at http://www.mathhelpboards.com/)
 
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A very interesting problem. Thank you @PotW Tobor :) I basically googled the answer, where a video showed a related problem of how to compute the ratio of the sum of the p-series divided by the alternating p-series.
 

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