Question Number 50395 by Abdo msup. last updated on 16/Dec/18
$${let}\:{U}_{{n}} =\left({e}−\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}} \right)^{\sqrt{{n}^{\mathrm{2}} \:+\mathrm{2}}−\sqrt{{n}^{\mathrm{2}} \:+\mathrm{1}}} \\ $$$${calculate}\:{lim}_{{n}\rightarrow+\infty} \:\:{U}_{{n}} \\ $$