Test convergence of series: $$\sum_{n=0}^ \infty n!z^n$$
What I have done using ratio test:
$\lim_{n\to\infty} \lvert \frac{(n+1!)(z^{n+1})}{n!z^n}\rvert$
$\lim_{n\to\infty} \lvert (n+1)(z)\rvert$
And here I am kinda stuck. Do I plug in $\infty$ for n and get $\infty$ as the answer?
If $L=\infty$ then it diverges since $L>1$?