What is another infinite series summation for Pi^2/6 besides 1/n^2?

  1. So the title pretty much says it all, what other infinite series summations do we have for Pi^2/6 besides,

    $$\sum_{n=1}^{\infty} 1/n^2$$

    ***EDIT*** I should also include,

    $$\sum_{n=1}^{\infty} 2(-1)^(n+1)/n^2$$
    $$\sum_{n=1}^{\infty} 4/(2n)^2$$
    etc. etc.

    A unique form outside of the 1/n^2 family.
     
    Last edited: Jan 13, 2014
  2. jcsd
  3. http://www.wolframalpha.com/input/?i=Pi^2%2F6
     
    1 person likes this.
  4. Office_Shredder

    Office_Shredder 4,499
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  5. Interesting, all of their series still have a 'squared' term for the denominator in some form or another. Do you know of any outside of the 1/n^2 family?

    Either way thanks for the link!

    That thread was about finding infinite series summations for 1/5 and 1/7 which eventually led to a 'general solution' for all '1/k' fractions for infinite series. This thread is specifically for Pi^2/6 and finding infinite series that are not of the 1/n^2 family.

    Hope this helps.
     
  6. Office_Shredder

    Office_Shredder 4,499
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    Take any series that equals 1/5 and multiply it by [itex] \frac{ 5 \pi^2}{6} [/itex].
     
  7. Yes, that would do it too...
    Do you have anything else besides Boreks standard answer on these things? :)

    On a more serious note (sort of), deriving these new series is a blast! I have not encountered any other subject in mathematics that has been more fun!
     
    Last edited: Jan 14, 2014
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