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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 .

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.