Answer
First five terms: $0, \frac{\ln2}{2}, \frac{\ln3}{3}, \frac{\ln4}{4}, \frac{\ln5}{5}$. This sequence converges to $0$.
Work Step by Step
Putting the values of $n={1,2,3,4,5}$ in $\frac{\ln n}{n}$ leads to the first five terms of the sequence. Note: $\ln 1 = 0$.
The limit $\lim_{n\to\infty} \frac{\ln n}{n}$ is of $\frac{\infty}{\infty}$ form. Using L’Hôpital’s rule,
$$\lim_{n\to\infty} \frac{\ln n}{n} = \lim_{n\to\infty} \frac{1}{n}=0$$.
Thus the sequence converges to $0$.
