# Math Help - convergence of a series

1. ## convergence of a series

Does the series SIGMA (0 to infinity) r!/r^2(e^r) converge or diverge and why?

Tried using the ratio test and got to lim (r tend to inf) r^2/(r+1)e , which equals infinity(?). sooo it diverges as its greater than 1?

2. You are correct

3. By the Stirling formula, $\frac{r!}{r^2e^r}$ does not tend to 0 as r approches infinity, thus the series diverges.