Question

Determine whether the series converges or diverges.

Answer 1

\[\sum_{n=1}^{\infty}\frac{ \ln n }{ n^2 }\]

Answer 2

I assume I use the limit test for convergence/divergence?

Answer 3

Because that clearly goes to 0. So therefore, the sum converges.

Answer 4

use integral test.

Answer 5

I know I could use integral test but could I also use limit test? Seems easier.

Answer 6

wait is the limit test the one that says that if the limit of \(a_n\) is NOT equal to 0, then it diverges?

Answer 7

Yeah.

Answer 8

no that is nth term test also called divergent test

Answer 9

Ohh. Our prof calls it the limit test.

Answer 10

Well you can't conclude if it gives 0... the converse of the statement is not true

Answer 11

According to my textbook: