# Math Table or Method of Solving an infinite sum of reciprocal powers

by pasqualrivera
Tags: infinite sums
 P: 2 Is anybody aware of how to solve the following infinite sum: $$\sum\frac{1}{n^2}$$ 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.
 P: 2,179 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