How do you determine whether the sequence #a_n=n/(ln(n)^2# converges, if so how do you find the limit?
Note: The question is not mentioning it expressly, but in the answer, I assume the series starts from
A necessary condition for any series to converge is Cauchy's condition that:
To verify whether this condition is met, first we note that
So if the limit
is the inderminate form
which implies that the series is not convergent.
As it has positive terms, the series is then divergent.