# How do you determine whether the sequence #a_n=n/(ln(n)^2# converges, if so how do you find the limit?

##### 1 Answer

The series:

is divergent.

#### Explanation:

**Note**: *The question is not mentioning it expressly, but in the answer, I assume the series starts from* *as* *is undefined for*

A necessary condition for any series to converge is Cauchy's condition that:

To verify whether this condition is met, first we note that

where

So if the limit

Now:

is the inderminate form

Thus also:

which implies that the series is not convergent.

As it has positive terms, the series is then divergent.