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let-f-x-k-2-1-k-x-k-1-find-D-f-2-let-put-x-n-1-1-n-n-x-Rieman-alternate-serie-find-f-x-interms-of-x-




Question Number 30480 by abdo imad last updated on 22/Feb/18
let f(x)= Σ_(k=2) ^∞   (((−1)^k )/(x+k))  1) find D_f   2)let put δ(x)= Σ_(n=1) ^∞   (((−1)^n )/n^x )  (Rieman alternate serie)  find f(x) interms of δ(x).
$${let}\:{f}\left({x}\right)=\:\sum_{{k}=\mathrm{2}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{x}+{k}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right){let}\:{put}\:\delta\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{{x}} }\:\:\left({Rieman}\:{alternate}\:{serie}\right) \\ $$$${find}\:{f}\left({x}\right)\:{interms}\:{of}\:\delta\left({x}\right). \\ $$

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