Answer
See below.
Work Step by Step
The six most common sequences are defined as below:
1) $\lim\limits_{n \to \infty}\dfrac{\ln n }{n}=0$
2) $\lim\limits_{n \to \infty} x^{1/n}=0 (x \lt 0)$
3) $\lim\limits_{n \to \infty}(1+\dfrac{x }{n})^n=e^x$ ; for any value of $x$.
4) $\lim\limits_{n \to \infty} \sqrt[n] n=1$
5) $\lim\limits_{n \to \infty} x^n =0$ ; for $-1 \lt x \lt 1$ or, $|x| \gt 1$.
6) $\lim\limits_{n \to \infty} \dfrac{x^n }{n!}=0$ ; for any value of $x$.
