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

[mesa]

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.

 

[dipole]

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

 

[Office_Shredder]

How is this thread different than the one you posted before?

https://www.physicsforums.com/showthread.php?t=730791

 

[mesa]

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!

How is this thread different than the one you posted before?

https://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.

 

[Office_Shredder]

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}.

 

[mesa]

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!