![\displaystyle \rm \red{ \sum_{k = 1}^{ \infty } \frac{( - 1 {)}^{k - 1} }{k} \sum_{n = 0}^{ \infty } \frac{1}{k {2}^{n} + 1} } \ \textless \ br /\ \textgreater \](https://tex.z-dn.net/?f=%5Cdisplaystyle+%5Crm+%5Cred%7B+%5Csum_%7Bk+%3D+1%7D%5E%7B+%5Cinfty+%7D+%5Cfrac%7B%28+-+1+%7B%29%7D%5E%7Bk+-+1%7D+%7D%7Bk%7D+%5Csum_%7Bn+%3D+0%7D%5E%7B+%5Cinfty+%7D+%5Cfrac%7B1%7D%7Bk+%7B2%7D%5E%7Bn%7D+%2B+1%7D+%7D+%5C++%5Ctextless+%5C+br+%2F%5C++%5Ctextgreater+%5C+ "\displaystyle \rm \red{ \sum_{k = 1}^{ \infty } \frac{( - 1 {)}^{k - 1} }{k} \sum_{n = 0}^{ \infty } \frac{1}{k {2}^{n} + 1} } \ \textless \ br /\ \textgreater \")
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tex]\displaystyle \rm \red{ \sum_{k = 1}^{ \infty } \frac{( - 1 {)}^{k - 1} }{k} \sum_{n = 0}^{ \infty } \frac{1}{k {2}^{n} + 1} } \ \textless \ br /\ \textgreater \ [/tex]
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