Question Number 29984 by abdo imad last updated on 14/Feb/18
$${prove}\:{that}\:\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{{H}_{{n}} }{{n}!}=={e}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(\mathrm{1}\right)^{\boldsymbol{{n}}−\mathrm{1}} }{\boldsymbol{{n}}\:\left(\boldsymbol{{n}}!\right)}\:. \\ $$