Příklad 2.37

Spočtěte \(\Large\lim_{x\to\infty}\left(1+\frac{1}{n}\right)^n+\sqrt[n]{10^6}+\left(\frac{99}{100}\right)^n\)

$$\Large \begin{aligned}

&\lim_{x\to\infty}\left(1+\frac{1}{n}\right)^n+\sqrt[n]{10^6}+\left(\frac{99}{100}\right)^n \

=& \lim_{x\to\infty}\left(1+\frac{1}{n}\right)^n+\lim_{x\to\infty}\sqrt[n]{10^6}+\lim_{x\to\infty}\left(\frac{99}{100}\right)^n \

=& e + 1 + 0\

=& \;\boxed{e + 1}

\end{aligned} $$