Science:Math Exam Resources/Courses/MATH101/April 2017/Question 06 (b)/Solution 1
Apply the ratio test. Since we have and
the following three situations are given
Therefore, for , we have , so that the series converges.
Now, we determine the convergence of series when .
When and , we have
Since in both case, , by the divergence test, the series doesn't converges.
To summarize, the series converges on