Science:Math Exam Resources/Courses/MATH101/April 2016/Question 10 (b)
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Question 10 (b) 

Define . Use the Ratio Test to answer the question: for which values of does the Maclaurin 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! 
Hint 

Recall the Ratio test: the series converges if What is in our problem? Compute the limit. 
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. We set and use the Ratio Test. Since
no matter what is, the series converges for all . 