Previous in Relation and Functions Next in Relation and Functions
Question Number 32487 by abdo imad last updated on 25/Mar/18
$${let}\:{x}>\mathrm{1}\:{and}\:\xi\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{{x}} }\:\left({zeta}\:{function}\:{of}\:{Rieman}\right) \\ $$ $$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} \xi\left({x}\right) \\ $$ $$\left.\mathrm{2}\right){let}\:{consider}\:\:{s}\left({x}\right)=\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\frac{\xi\left({n}\right)}{{n}}\:{x}^{{n}} \:{study}\:{the}\:{convergence} \\ $$ $${of}\:{s}\left({x}\right)\:{and}\:{find}\:{a}\:{simple}\:{form}\:{of}\:{s}\left({x}\right). \\ $$