Science:Math Exam Resources/Courses/MATH307/December 2012/Question 04 (d)
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Question 04 (d) 

Consider the Fourier series for . (d) Given that for , use Parseval's formula to find the value of the infinite sum . Calculate a numerical expression  you do not need to simplify your answer. 
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 

Parseval's formula says that Calculate the integral on the left hand side and plug in the given and calculated values for c_{n} on the right hand side. Then, isolate for 
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. Consider the Fourier series for . Parseval’s formula says Plugging in the left hand side we calculate Plugging in the given and calculated values for c_{n} in the right hand side we compute Combining the left hand side and the right hand side of Parseval's formula we can find Therefore, the infinite sum is 