# convergence of $\sum _{n=1}^\infty \frac{\cos(n!)}{n}$, $\sum _{n=1}^\infty \frac{\sin(n!)}{n}$

if it is difficult to discuss n!, maybe we can change n! into $$\Gamma(n+1)$$.

$$\Gamma(z+1)=\int \limits_{0}^\infty t^ze^{-t}dt$$