ANA1_L12

If $p>0$, then ${\lim }_{n\to \infty }\frac{1}{n^p}=0$.
If $p>0$, then ${\lim }_{n\to \infty }\sqrt[n]{p}=1$.
${\lim }_{n\to \infty }\sqrt[n]{n}=1$.
If $p>0$ and $\alpha$ is real, then ${\lim }_{n\to \infty }\frac{n^{\alpha }}{(1+p{)}^n}=0$.
If $|x|<1$, then ${\lim }_{n\to \infty }{x}^n=0$.