Science:Math Exam Resources/Courses/MATH105/April 2017/Question 05 (b)
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Question 05 (b) 

Let be the Maclaurin series for , i.e., . Find for all . 
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 

In order to solve this problem, you do NOT want to compute the Maclaurin series by repeatedly taking derivatives. Instead, you should aim to apply the geometric series formula 
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 want to find the MacLaurin series for the function 