Question Number 33337 by prof Abdo imad last updated on 14/Apr/18
$${let}\:\alpha>\mathrm{0}\:{prove}\:{that} \\ $$$$\sum_{{k}=\mathrm{1}} ^{{n}} \:\left(\mathrm{1}−\alpha\frac{{k}}{{n}}\right)_{{n}\rightarrow\infty} ^{{n}} \rightarrow\:\frac{{e}^{−\alpha} }{\mathrm{1}−{e}^{−\alpha} } \\ $$