Why is it true that $$\sum\limits_{k=2}^{n}{k \over \ln k} \le {n^2 \over \ln n}, n \ge 2$$
I try to expand the term of the sum in taylor series but it didn't help me.
I try to recognize the sum as a lower Riemman sum of $\int{x \over lnx}$, but it didn't help either.