Science:Math Exam Resources/Courses/MATH103/April 2017/Question 04/Solution 1

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Let

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

.

Since

,

by the Term Test for divergence, the series diverges when . Thus, the answer is as follows.