Question

Does the series: \sum_{n=2}^{\infty} n/ln (n) converge or diverge? What test do I use?

Answer 1

well, you can remember that lim(n/lnn) is infinity when n goes to infinity so the series diverges

Answer 2

\[\sum_{n=2}^{\infty} \frac{n}{\ln n} diverges\ since\ for\ a_{n} = \frac{n}{\ln n} \ we\ have \lim_{n \rightarrow \infty} \ a_{n} =\lim_{n \rightarrow \infty} \frac{1}{\frac{1}{n}} \rightarrow \infty\]

Answer 3

that's correct :D the good thing to know is if lim of an doesn't go to zero when n goes to infinity that's sufficient to conclude that your sum diverges....

Answer 4

Thanks, your hint helped a lot.

Answer 5

you're welcome :D