Answer
Diverges.
Work Step by Step
Given $$ \sum_{n=1}^{\infty} (-1)^{n} n^2$$
Since
\begin{align*}
\lim _{n \rightarrow \infty} (-1)^{n} n^2\neq 0
\end{align*}
Since the $n$th term $a_{n}$ does not converge to zero, thus the series diverges.
