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Question Number 144307 by mohammad17 last updated on 24/Jun/21

$${lim}_{n\to \mathrm{\infty }}{(1+\frac{1}{n})}^p$$

Commented by mohammad17 last updated on 24/Jun/21

$$helpmesirplease$$

Answered by Dwaipayan Shikari last updated on 24/Jun/21

$$1$$

Answered by mathmax by abdo last updated on 25/Jun/21

$${\mathrm{U}}_{\mathrm{n}}={(1+\frac{1}{\mathrm{n}})}^{\mathrm{p}}\Rightarrow {\mathrm{U}}_{\mathrm{n}}={\mathrm{e}}^{\mathrm{plog}(1+\frac{1}{\mathrm{n}})}\sim {\mathrm{e}}^{\frac{\mathrm{p}}{\mathrm{n}}}\to 1(\mathrm{n}\to \mathrm{\infty })\mathrm{pour}\mathrm{p}\mathrm{fixe}$$$$\Rightarrow {\lim }_{\mathrm{n}\to +\mathrm{\infty }}{\mathrm{U}}_{\mathrm{n}}=1$$

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