Question Number 34695 by math khazana by abdo last updated on 09/May/18
$${let}\:{give}\:{U}_{{n}} =\:\left\{\frac{\mathrm{1}}{{n}}\:\prod_{{k}=\mathrm{1}} ^{{n}} \:\left(\alpha+{k}\right)\right\}^{\frac{\mathrm{1}}{{n}}} \\ $$$${find}\:{lim}_{{n}\rightarrow+\infty} \:\:{U}_{{n}} \:?. \\ $$