Science:Math Exam Resources/Courses/MATH101/April 2017/Question 06 (b)/Solution 1

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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

and

, respectively.

Since in both case, , by the divergence test, the series doesn't converges.

To summarize, the series converges on