The series
\sum_{k=1}^\infty \frac{\left(-3\right)^{k}}{k!}
is an alternating series but we can apply
the ratio test to
\sum_{k=1}^\infty\left\vert \frac{\left(-3\right)^{k}}{k!} \right\vert
to test for absolute convergence.
Applying the ratio test for absolute convergence
you would compute

\displaystyle \lim_{k \to \infty} \,
\biggl \lvert \dfrac {a_{k + 1}} {a_k}
\biggr \rvert = \lim_{k \to \infty}
= .

Hence the series
converges
converges absolutely
diverges
inconclusive
.

Note that you will have to simplify your answer for the limit or you will get an error message.

Hence the series

Note that you will have to simplify your answer for the limit or you will get an error message.

You can earn partial credit on this problem.