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. 

$$\sum_{n=1}^{\infty}\frac{19}{n!}=19\left(1+\sum_{n=2}^{\infty}\frac{1}{n!}\right)<19\left(1+\sum_{n=1}^{\infty}\frac{1}{n(n+1)}\right)=$$
$$=19\left(1+\sum_{n=1}^{\infty}\left(\frac{1}{n}-\frac{1}{n+1}\right)\right)=19(1+1)=38.$$
Thus, our series converges.
