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

by mesa
Tags: 1 or n2, infinite, pi2 or 6, series, summation
 P: 491 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.
 P: 418 http://www.wolframalpha.com/input/?i=Pi^2%2F6
 Mentor P: 4,499 How is this thread different than the one you posted before? http://www.physicsforums.com/showthread.php?t=730791
P: 491

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

 Quote by dipole http://www.wolframalpha.com/input/?i=Pi^2%2F6
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!

 Quote by Office_Shredder How is this thread different than the one you posted before? http://www.physicsforums.com/showthread.php?t=730791
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.
Mentor
P: 4,499
 Quote by mesa 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.
Take any series that equals 1/5 and multiply it by $\frac{ 5 \pi^2}{6}$.
P: 491
 Quote by Office_Shredder Take any series that equals 1/5 and multiply it by $\frac{ 5 \pi^2}{6}$.
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!

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