Answer
The limit does not exit.
Work Step by Step
We have to compute the limit of the absolute value as follows
$$
\lim _{n \rightarrow \infty}| (-1)^na_n|= \lim _{n \rightarrow \infty}a_n
=2\neq 0.
$$Since the limit of the absolute value is non-zero, then the limit does not exit.
