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Question Number 30439 by abdo imad last updated on 22/Feb/18

let F(x)=Σ_(n=1) ^∞   (((−1)^(n−1) )/n^x )  calculate (dF/dx)(x).

$${let}\:{F}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} }{{n}^{{x}} }\:\:{calculate}\:\frac{{dF}}{{dx}}\left({x}\right). \\ $$

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