Question Number 114858 by Eric002 last updated on 21/Sep/20
$${prove} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left({H}_{{k}} \right)^{\mathrm{2}} }{{k}\mathrm{2}^{{k}} }=\frac{\mathrm{7}\zeta\left(\mathrm{3}\right)}{\mathrm{8}} \\ $$