Question Number 152447 by fotosy2k last updated on 28/Aug/21
Commented by fotosy2k last updated on 28/Aug/21
$${pls}\:{help}\:{me} \\ $$
Answered by EDWIN88 last updated on 28/Aug/21
![lim_(n→∞) [(1+(1/n))]^(n+3) =e^(lim_(n→∞) (1+(1/n)−1).n+3) = e^(lim_(n→∞) (((n+3)/n))) =e^1 =e](https://www.tinkutara.com/question/Q152458.png)
$$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left[\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)\right]^{{n}+\mathrm{3}} \:={e}^{\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}−\mathrm{1}\right).{n}+\mathrm{3}} \\ $$$$=\:{e}^{\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{{n}+\mathrm{3}}{{n}}\right)} ={e}^{\mathrm{1}} ={e} \\ $$
Commented by fotosy2k last updated on 30/Aug/21
$${thank}\:{you} \\ $$