Question Number 26573 by abdo imad last updated on 26/Dec/17
$${let}\:{put}\:\:{H}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{k}={n}} \:\:\frac{\mathrm{1}}{{k}}\:\:\:\:\:\:{prove}\:{that}\:\:\:\sum_{{n}=\mathrm{1}} ^{\propto} \:\frac{{H}_{{n}} }{{n}^{\mathrm{2}} }\:\:=\:\:\mathrm{2}\xi\left(\mathrm{3}\right) \\ $$