calculus - How can I show that $sum limits_{n=2}^inftyfrac{1}{nln n}$ is divergent without using the integral test?

How can I show that $\sum \limits_{n=2}^\infty\frac{1}{n\ln n}$ is divergent without using the integral test?

I tried using the comparison test but I could not come up with an inequality that helps me show the divergence of a series. I also tried using the limit comparison test but I was not successful.

Please do not give me solutions; just a hint so that I can figure it out myself.