Answer
Diverges
Work Step by Step
Formula to calculate the sum of a geometric series is:
$S=\dfrac{a}{1-r}$;
Consider the series $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} \dfrac{n!}{1000^n}$ .
Here, the numerator terms will be increased more than the terms on denominator.
Also, $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} \dfrac{n!}{1000^n}=\infty \ne 0$
Hence, the series diverges.
