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let-U-n-e-1-1-n-n-n-2-2-n-2-1-calculate-lim-n-U-n-




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

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