Science:Math Exam Resources/Courses/MATH103/April 2016/Question 08 (c)
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Question 08 (c) 

Find the Taylor series for about . State (without proof) for which values of this power series converges. 
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 if has a radius of convergence , then we can do termbyterm integration and this series also have a radius of convergence . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. By the part (a), we have with infinity radius of convergence. Then, by using the fact in Hint 1, we can do term by term integration and the last power series also have infinity radius of convergence. i.e., converges at any point on the real line.

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