Finding the sum of this p-series

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SUMMARY

The sum of the p-series 1/n^2 from n = 1 to infinity is known as the Basel Problem, which was first solved by mathematician Leonhard Euler. The most straightforward method to derive this sum is through the use of Fourier series. Various proofs and approaches to this problem can be found on the Wikipedia page dedicated to the Basel Problem.

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  • Understanding of p-series convergence
  • Familiarity with Fourier series
  • Basic knowledge of calculus
  • Awareness of historical mathematical problems, specifically the Basel Problem
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  • Study the derivation of the Basel Problem using Fourier series
  • Explore alternative proofs of the Basel Problem
  • Learn about the implications of the Basel Problem in number theory
  • Investigate related series and their convergence properties
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This discussion is beneficial for mathematics students, educators, and anyone interested in series convergence and historical mathematical problems.

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Homework Statement


How do you find the sum of the p-series 1/n^2 from n = 1 to infinity? My friend asked me this question and I was completely stumped; I have no leads on what you are suppose to do to solve this. I would be glad if you guys could give me hints as to how to begin solving.

Homework Equations


Not sure what is used to solve this

The Attempt at a Solution

 
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This is called the Basel Problem, and it was first solved by Euler. There are several ways of solving it; I think the easiest is with a Fourier series. There are severla proofs here:
http://en.wikipedia.org/wiki/Basel_problem
 

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