If $f\left(x\right)\=\frac{\ln \left(x\right)}{x}$, then $f\left(n\right)\=a_n$. Hence, the limit of $f\left(x\right)$ as $x\to \infty$ will be the limit of the sequence.

L'Hôpital's rule is a suitable tool for computing $\underset{x\to \infty }{lim}\frac{\ln \left(x\right)}{x}\=\underset{x\to \infty }{lim}\frac{1\/x}{1}\=\underset{x\to \infty }{lim}\frac{1}{x}\=0$. 

Hence, $\underset{n\to \infty }{lim}\frac{\ln \left(n\right)}{n}\=0$.

Table 8.1.2(a) contains the  task template that, given the general term of a sequence, calculates and graphs its first few members.

Place the cursor somewhere in the cell containing the phrase "General term"and press the Tab key often enough for the cursor to move to, and select the default general term. With this expression auto-selected, simply overwrite with the desired general term, most easily obtained by a copy/paste operation. Then, adjust any of the inputs as needed, and simply press the Enter key to execute each command in the template.