real analysis - How do i evaluate this sum $sumlimits_{n=1}^{infty} frac{(-1)^{n+1}}{n^2n!}$?

How do I evaluate this sum:
$$\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^2n!}$$

Note: The series converges by the ratio test. I have tried to use this sum: $$\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}= \ln (2)$$ but I didn't succeed. Might there be others techniques which I don't know?

Thank you for any help