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How does one prove the zeta function identity

$$\sum_{s=2}^{\infty}\left(1-\sum_{n=1}^{\infty}\frac{1}{n^s}\right)=-1 \;?$$

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    We have to deal with the problem of whether interchanging the order of summation is legitimate (sometimes it isn't).2012-02-09

1 Answers 1