Science:Math Exam Resources/Courses/MATH105/April 2014/Question 02 (b)
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Question 02 (b) 

Find the radius of convergence of the power 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! 
Hint 

Recall that the radius of convergence for a series can be found by determining the range of xvalues where the series converges absolutely. The ratio test will give you information about absolute convergence. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let be the terms in the series. From the ratio test, we are guaranteed absolute convergence when . With , we have and thus We recall that and thus in general . This also means that . Thus,
Computing for all x. Hence, the series converges absolutely for all xvalues and the radius of convergence is . 