MATH101 April 2017
• Q1 (a) • Q1 (c) • Q1 (d) • Q2 (a) • Q2 (b) • Q2 (c) (i) • Q2 (c) (ii) • Q2 (c) (iii) • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q8 • Q9 • Q10 • Q11 (a) • Q11 (b) • Q11 (c) •
Question 06 (b)
For which values of x does the series converge?
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
Use the ratio test to determine the intervals where this series converge
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Apply the ratio test. Since we have
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