1. ## direct comparison test

Hi. I need to show whether this series diverges or converges, by the direct comparison test. But I don't understand what it is that I should compare it to that is helpful.

$\sum_{n=2}^{\infty}\frac{ln\,n}{n+1}$

2. ## Re: direct comparison test

Since for $n\ge{3}$, $\ln{n}\ge{1}$ and $2n>n+1$, $\frac{\ln{n}}{n+1}>\frac{1}{2n}$.

- Hollywood

3. ## Re: direct comparison test

Why not just compare it to $\sum{\frac{1}{n+1}}$?