Answer like a college student in calculus with analytical geometry. Please show all work.

Use the Integral test to determine if the series converges or diverges.

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{nln(n)}$

Use the comparison test to determine if the series converges or diverges.

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{1}{n^{3}1}$

Use the limit comparison test to determine if the series converges or diverges.

${\displaystyle \underset{n=1}{\overset{}{}}}\frac{n^{2}2n}{n^{3}3n^{2}2}$