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

Not sure if the question is about $1^n$ or $(-1)^n$ but in the latter case :
Hint: you have to group terms by two : $\sum \frac{1}{\ln(2n)} - \frac{1}{\ln(2n+1)}$.
Then use the $O()$ notation and express $\ln(2n+1)$ in terms of $\ln(2n)$ and $O(\frac{1}{n})$
This should lead you to $\sum O(\frac{1}{n\ln(n)})$. If you are not familiar with this notation I will answer more
