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Question Number 26573 by abdo imad last updated on 26/Dec/17

let put  H_n = Σ_(k=1) ^(k=n)   (1/k)      prove that   Σ_(n=1) ^∝  (H_n /n^2 )  =  2ξ(3)

$${let}\:{put}\:\:{H}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{k}={n}} \:\:\frac{\mathrm{1}}{{k}}\:\:\:\:\:\:{prove}\:{that}\:\:\:\sum_{{n}=\mathrm{1}} ^{\propto} \:\frac{{H}_{{n}} }{{n}^{\mathrm{2}} }\:\:=\:\:\mathrm{2}\xi\left(\mathrm{3}\right) \\ $$

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