Consider the series
Determine whether the series converges or diverges. If it converges, determine whether it converges conditionally or absolutely.
The series converges.
Proof. Let . Then, the series converges since it is of the form for . Using the limit comparison test we have
Hence, the series and both converge or both diverge. Since converges we have establish the convergence of
You need to prove $a_n>0$ for all $n>0$ (which, of course, if trivial) to use the Comparison Test.