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