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solve-n-1-H-n-n-2-2-n-




Question Number 112867 by mathdave last updated on 10/Sep/20
solve  Σ_(n=1) ^∞ (H_n /(n^2 2^n ))
$${solve} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} }{{n}^{\mathrm{2}} \mathrm{2}^{{n}} } \\ $$
Commented by mnjuly1970 last updated on 10/Sep/20
hello mr dave   is correct the final answer?  ζ(3) −((ln(2)π^2 )/(12))
$${hello}\:{mr}\:{dave} \\ $$$$\:{is}\:{correct}\:{the}\:{final}\:{answer}? \\ $$$$\zeta\left(\mathrm{3}\right)\:−\frac{{ln}\left(\mathrm{2}\right)\pi^{\mathrm{2}} }{\mathrm{12}} \\ $$$$ \\ $$
Commented by mathdave last updated on 11/Sep/20
yah u re correct
$${yah}\:{u}\:{re}\:{correct} \\ $$
Answered by mnjuly1970 last updated on 10/Sep/20
Commented by Tawa11 last updated on 06/Sep/21
great sir
$$\mathrm{great}\:\mathrm{sir} \\ $$
Answered by mnjuly1970 last updated on 10/Sep/20
Commented by mathdave last updated on 10/Sep/20
nice work
$${nice}\:{work} \\ $$
Commented by mnjuly1970 last updated on 10/Sep/20
thank you so much mr  dave ..grateful..
$${thank}\:{you}\:{so}\:{much}\:{mr} \\ $$$${dave}\:..{grateful}.. \\ $$

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