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Putnam 2016 B6

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Riemann
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Putnam 2016 B6

#1

Post by Riemann » Mon Dec 05, 2016 12:57 pm

Evaluate the sum

$$\sum_{m=1}^{\infty}\frac{(-1)^{m-1}}{m}\sum_{n=0}^{\infty}\frac{1}{m2^n+1}$$
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$
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