practice
\[ \begin{aligned} &\lim_{n \to \infty} \sqrt[n]{n} \\ a_n &= \sqrt[n]{n} - 1 \\ (a_n + 1) ^ n &= n \\ \binom{n}{2}a_n^{n-2} &\le n \\ a_n &\le \frac{2}{n-1}\\ \lim_{n \to \infty} \sqrt[n]{n} &= 1 \end{aligned} \]
\[ \begin{aligned} &\lim_{n \to \infty} \sqrt[n]{n} \\ a_n &= \sqrt[n]{n} - 1 \\ (a_n + 1) ^ n &= n \\ \binom{n}{2}a_n^{n-2} &\le n \\ a_n &\le \frac{2}{n-1}\\ \lim_{n \to \infty} \sqrt[n]{n} &= 1 \end{aligned} \]