Answer:
The test is inconclusive.
Explanation:
Let us assume that the series is
. The Divergence Test tell us that, if the limit of the sequence defined by the general term of the series:
, is different from zero, or it doesn't exist, then the series diverges.
In this exercise we have
, then the limit we want to study is

It is not difficult to see that if
grows to infinity,the limit of the given fraction is zero:

Thus, the convergence test is inconclusive. Recall the case of the harmonic series:
, which is divergent and clearly
.