Test the following series for convergence or divergence. Justify the decision.
The series converges. To show this, first we note that
Thus, if we can show that the series
converges then the series in question converges by the comparison test. To show that this series converges we apply the limit comparison test with
We know that converges since it is of the form for . Furthermore,
for . Thus,
converges which implies the convergence of