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let-x-n-1-1-n-x-prove-that-x-1-x-1-o-1-




Question Number 30438 by abdo imad last updated on 22/Feb/18
let ξ(x)= Σ_(n=1) ^∞  (1/n^x ) prove that   ξ(x)= γ +(1/(x−1)) +o(1).
$${let}\:\xi\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{{x}} }\:{prove}\:{that}\: \\ $$$$\xi\left({x}\right)=\:\gamma\:+\frac{\mathrm{1}}{{x}−\mathrm{1}}\:+{o}\left(\mathrm{1}\right). \\ $$

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