Answer
Diverges
Work Step by Step
Consider $u_n=(-1)^{n+1}\dfrac{n!}{2^n}$
Here, $u_n$ is positive for all the values of $n$.
Now $\lim\limits_{n \to \infty} \dfrac{n!}{2^n}=\infty$
Hence, the series diverges by the nth Term Test.
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