## University Calculus: Early Transcendentals (3rd Edition)

The sum of a geometric series can be found as: $S=\dfrac{a}{1-r}$ We are given $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} \dfrac{n!}{1000^n}$ . In the given series, the numerator increases faster than the denominator: Thus, we have $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} \dfrac{n!}{1000^n}=\infty \ne 0$ Now, $s_n \to \infty$ as $n \to \infty$, so, the given series diverges.