Science:Math Exam Resources/Courses/MATH103/April 2017/Question 04/Solution 1
Use the Ratio Test. This requires us to calculate . Doing so, we obtain,
One can check that
So by the Ratio Test, the sum converges if and the sum diverges if .
When (i.e., or ), the sum becomes
by the Term Test for divergence, the series diverges when . Thus, the answer is as follows.