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Question Number 114858 by Eric002 last updated on 21/Sep/20

prove  Σ_(k=1) ^∞ (((H_k )^2 )/(k2^k ))=((7ζ(3))/8)

$${prove} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left({H}_{{k}} \right)^{\mathrm{2}} }{{k}\mathrm{2}^{{k}} }=\frac{\mathrm{7}\zeta\left(\mathrm{3}\right)}{\mathrm{8}} \\ $$

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