MATH103 April 2015
• Q1 (a) (i) • Q1 (a) (ii) • Q1 (a) (iii) • Q1 (b) (i) • Q1 (b) (ii) • Q1 (b) (iii) • Q1 (c) (i) • Q1 (c) (ii) • Q1 (c) (iii) • Q1 (d) (i) • Q1 (d) (ii) • Q1 (e) (i) • Q1 (e) (ii) • Q1 (e) (iii) • Q2 (a) • Q2 (b) • Q2 (c) • Q2 (d) • Q2 (e) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q6 (c) • Q7 (a) • Q7 (b) • Q7 (c) • Q7 (d) • Q8 • Q9 • Q10 (a) • Q10 (b) •
Question 01 (b) (iii)
Determine whether the following series converge or diverge. (do not calculate the value of converging series.)
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 Comparison Test.
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We can rewrite the series as . Note that since is an increasing function, and since and , we have that function for all , so
We now can compare our series with which is convergent due to the p-Test. So,
Since is convergent, the comparison test implies that is also convergent.