Science:Math Exam Resources/Courses/MATH103/April 2016/Question 07 (b) (i)
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Question 07 (b) (i) 

Consider the power series: . (i) 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 

Apply the ratio test. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let and apply the ratio test: Therefore, the given series converges when (i.e., ) and diverges when (i.e., ). In other words, the radius of convergence is 