Science:Math Exam Resources/Courses/MATH101/April 2014/Question 01 (h)
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Question 01 (h) 

Short Problem. Show your work. No credit will be given for the answer without the correct accompanying work. Find a power series representation for . 
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 

One of the common power series is ? How can we use this to our advantage? 
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. By geometric series, we have, for ,
Multiplying both sides by yields
which is the power series we are looking for. 