Find convergence of series .... How do we find the convergence of $$ s_n = \sin (1!) +  \frac {\sin (2!)}{1!} + \frac {\sin (3!)}{2!} + \frac {\sin (4!)}{3!} +... \frac {\sin (n+1!)}{n!} $$ 
I was thinking of using convergence tests but they are used only for infinite series.  I tried to use the ratio test $ \frac {a_{(n+1)}}{a_n}$ but the series does not go to infinite so I couldn't use it. Meanwhile I also tried to simplify it, but still I couldn't get something concrete.

Hint
$$\left|\frac{\sin((k+1)!)}{k!}\right|\le\frac{1}{k!}$$
