Answer
The sequence is not monotonic. The sequence is bounded.
Work Step by Step
$a_{n}=2+\frac{(-1)^{n}}{n}$
$a_{1}=2+\frac{(-1)^{1}}{1}=1$
$a_{2}=2+\frac{(-1)^{2}}{2}=\frac{5}{2}$
$a_{3}=2+\frac{(-1)^{3}}{3}=\frac{5}{3}$.
$a_{2}\gt a_{1}$ but $a_{3}\lt a_{2}$, So the series is not monotonic.
We can see that $a_{n}\leq\frac{5}{2}$ for all $n\geq1$.
The sequence is bounded above.
We can also see that $1\leq a_{n}$ for all $n\geq1$.
The sequence is bounded below.
The sequence is bounded.
