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

  • Thread starter mesa
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  • #1
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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.
 
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Answers and Replies

  • #2
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http://www.wolframalpha.com/input/?i=Pi^2%2F6
 
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  • #4
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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.
 
  • #5
Office_Shredder
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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 [itex] \frac{ 5 \pi^2}{6} [/itex].
 
  • #6
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Take any series that equals 1/5 and multiply it by [itex] \frac{ 5 \pi^2}{6} [/itex].
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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