I am perfectly fine with determining whether a series converges or diverges as long as it doesn’t involve the natural logarithm. I am having trouble with finding out whether ln n/n^{2} converges or not. If compare it with 1/n^{2}, the test will fail. ln n is not a constant but it is very slow, so I figured that comparing it with 1/n^{3/2} could work. By using the limit Comparison Test, I keep getting wrong answers. The limit of (n^{3/2}*ln (n))/n^{2} as n approaches infinity is equivalent to the limit of ln n/sqrt(n) as n approaches infinity, and here I should use L’Hopital, so (1/n)/(1/2sqrt(n)). I will get an indeterminate form indefinitely (0/0). What should I do?

## picado

Hint: sqrt(n)/n = 1/sqrt(n)