## Thomas' Calculus 13th Edition

Let us consider $a_n=(-1)^{n+1}\dfrac{n!}{2^n}$ and $u_n$ refers to all positive values of $n$. Here, we have $\lim\limits_{n \to \infty} a_n=\lim\limits_{n \to \infty} \dfrac{n!}{2^n}=\infty$ Hence, the series diverges by the Nth Term Test.