# 2013 PMWC Problems/Problem I15

## Solution

First of all, note that , and that

Splitting into its even component and odd component, we can write as:

Simplifying, we see that

Therefore, the required answer is

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Revision as of 16:55, 13 January 2020 by Dividend (talk | contribs) (Created page with "==Solution== First of all, note that <math>M=\sum_{n=1}^\infty \frac{1}{k^2}</math>, and that <math>K=\sum_{n=1}^\infty \frac{1}{(2k-1)^2}</math> Splitting <math>M</math> in...")

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First of all, note that , and that

Splitting into its even component and odd component, we can write as:

Simplifying, we see that

Therefore, the required answer is

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