$$\sum \_{n=0}^{\infty }\:\frac{(1)^n}{\ln\left(n+1\right)}$$

I've tried using Ratio Test as it seems to be the most obvious but it doesn't work.

edit: actually it should be $1^n $ which is just 1. It was just a part of a question where I had to sub in x = 1 & x = -1 to find whether the end point converges or diverges.
sorry for misunderstanding