Science:Math Exam Resources/Courses/MATH101/April 2011/Question 01 (h)
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Question 01 (h) 

For this question, the exam asks to put your answer in the box provided but also to show your work. This question is worth 3 marks. Full marks is given for correct answers placed in the box and at most 1 mark is given for an incorrect answer. You are required to simplify your answers as much as possible. Find all real number so that the series is convergent: 
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! 
Hint 

What does the alternating series test tell you? 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The alternating series test says that, given a series where is a positive sequence such that , then we have that the series converges. In our case, so long as , this satisfies the conditions of the alternating series test and so it converges. For , the sequence does not converge to zero, and so the sequence diverges. Thus the series converges for all . 