Answer
The sequence is increasing and not bounded.
Work Step by Step
$a_{n} = n + \frac{1}{n}$
$f(x) = x + \frac{1}{x}$
$f'(x) = 1- \frac{1}{x^{2}}$
$=\frac{x^{2}-1}{x^{2}} \gt 0$ for $x \gt 1$
Thus $f$ is an increasing function $(1, \infty)$ and therefore {$a_{n}$} is an increasing sequence.
$\lim\limits_{n \to \infty} a_{n}$
$=\lim\limits_{n \to \infty} n + \frac{1}{n}$
$= \infty$
Therefore, the sequence is not bounded.