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let-give-x-n-1-1-n-x-prove-that-x-x-gt-1-2-x-




Question Number 26568 by abdo imad last updated on 26/Dec/17
let give ξ(x)= Σ_(n=1) ^∝ (1/n^x )  prove that ξ(x)−_(x−>∝) 1∼2^(−x)
$${let}\:{give}\:\xi\left({x}\right)=\:\sum_{{n}=\mathrm{1}} ^{\propto} \frac{\mathrm{1}}{{n}^{{x}} }\:\:{prove}\:{that}\:\xi\left({x}\right)−_{{x}−>\propto} \mathrm{1}\sim\mathrm{2}^{−{x}} \\ $$

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