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.

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

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- Mar 25th 2013, 08:06 PMinfraReddirect 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.

$\displaystyle \sum_{n=2}^{\infty}\frac{ln\,n}{n+1}$ - Mar 25th 2013, 08:23 PMhollywoodRe: direct comparison test
Since for $\displaystyle n\ge{3}$, $\displaystyle \ln{n}\ge{1}$ and $\displaystyle 2n>n+1$, $\displaystyle \frac{\ln{n}}{n+1}>\frac{1}{2n}$.

- Hollywood - Mar 25th 2013, 09:25 PMProve ItRe: direct comparison test
Why not just compare it to $\displaystyle \sum{\frac{1}{n+1}}$?