# Is $\sum_{n=1}^{\infty}\frac{(\log\log2)^n}{n!}>\frac{3}{5}$

Question is to check if : $\sum_{n=1}^{\infty}\frac{(\log\log2)^n}{n!}>\frac{3}{5}$

the problem is that i am sure that this series$\sum_{n=1}^{\infty}\frac{(\log\log2)^n}{n!}$ is convergent (if it is not then i would be very happy as i will then be done.)

I would be thankful if someone can help me out with solving this.