Math Table or Method of Solving an infinite sum of reciprocal powersby pasqualrivera Tags: infinite sums 

#1
Sep2810, 06:26 PM

P: 2

Is anybody aware of how to solve the following infinite sum:
[tex]\sum\frac{1}{n^2}[/tex] for all positive odd integers? Is this the sort of thing you just look up in a math table or solve? If math table, do I need a "sum of reciprocal powers" table or a "riemann zeta function" table? If solve  how? I know the answer is pi^2 / 8 but I haven't a clue how to calculate that and cannot find a math table with the appropriate functions. 



#2
Sep2810, 07:24 PM

P: 2,080

This is the Riemann zeta function Zeta(2), by definition. It's actually equal to pi^2/6, not pi^2/8, and Euler found a clever way of showing this, which is detailed here:
http://en.wikipedia.org/wiki/Basel_problem 



#3
Sep2810, 10:04 PM

Sci Advisor
HW Helper
Thanks
P: 25,175





#4
Sep2910, 07:25 AM

P: 2,080

Math Table or Method of Solving an infinite sum of reciprocal powers
Sorry, I missed the "odd". You're right.




#5
Sep2910, 03:35 PM

P: 2

That makes sense, since the even series is not hard to find. I was thinking about this earlier today and haven't done the calculation yet, but I'm glad to have some reinforcement on that path.
Now I get to have fun learning the even series. thx 


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