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Question Number 157219 by amin96 last updated on 21/Oct/21

Σ_(0<n) (((−1)^(n−1) n)/(sinh(πn)))=(1/(4π))    prove

$$\underset{\mathrm{0}<\boldsymbol{\mathrm{n}}} {\sum}\frac{\left(−\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}−\mathrm{1}} \boldsymbol{\mathrm{n}}}{\boldsymbol{\mathrm{sinh}}\left(\pi\boldsymbol{\mathrm{n}}\right)}=\frac{\mathrm{1}}{\mathrm{4}\pi}\:\:\:\:{prove} \\ $$

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