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What is another infinite series summation for Pi^2/6 besides 1/n^2? 
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#1
Jan1314, 11:35 PM

P: 553

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. 


#2
Jan1414, 01:44 PM

P: 436

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



#3
Jan1414, 01:50 PM

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How is this thread different than the one you posted before?
http://www.physicsforums.com/showthread.php?t=730791 


#4
Jan1414, 07:01 PM

P: 553

What is another infinite series summation for Pi^2/6 besides 1/n^2?
Either way thanks for the link! Hope this helps. 


#5
Jan1414, 07:37 PM

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#6
Jan1414, 08:25 PM

P: 553

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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