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- Thread starter Hertz
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- #2

mathman

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http://ptrow.com/articles/Infinite_Series_Sept_07.htm

Above describes the derivation of

$$\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}$$

Your equation is readily derived from this. Add all the $$\frac{1}{(2n)^2}$$ terms to your series and then subtract that series as [itex](\sum_{n=1}^{\infty}\frac{1}{n^2})/4[/itex]. You end up with $$\frac{\pi^2}{6}-\frac{1}{4}\frac{\pi^2}{6}=\frac{\pi^2}{8}$$

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Thanks!

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- #4

WWGD

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I know the proof is written in detail in Dunham's "Journey Through Genius".

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