# Chapter 9 - Section 9.6 - Alternating Series and Conditional Convergence - Exercises - Page 521: 20

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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