# direct comparison test

• March 25th 2013, 09:06 PM
infraRed
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.

$\sum_{n=2}^{\infty}\frac{ln\,n}{n+1}$
• March 25th 2013, 09:23 PM
hollywood
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
• March 25th 2013, 10:25 PM
Prove It
Re: direct comparison test
Why not just compare it to $\sum{\frac{1}{n+1}}$?