Determine whether the series converges or diverges. Determine whether the series converges or diverges. 
$$
 \sum _{n=1}^{\infty }\:\left(\frac{19}{n!}\right)
$$
I know that this question a lot easier if I use ratio test but I  have not learned ratio test yet. The only option I have is divergence, comparison, limit comparison, and integral test. How can I prove that this series converges by using the limited tests. 
Thanks in advance. 

Then use the fact that $(\forall n\in\mathbb{N}\setminus\{2,3\}):\frac{19}{n!}\leqslant\frac{19}{n^2}$ and apply the integral test in order to prove that $\sum_{n=1}^\infty\frac{19}{n^2}$ converges.
