1. The problem statement, all variables and given/known data Hi everyone. I have a Fourier series problem from an old Physics GRE that I would like to discuss. Here is a link to the problem and a solution. The answer they get is correct, but their explanation is not: http://grephysics.net/ans/9277/39 2. Relevant equations Fourier Analysis, but we should be able to solve this without too much math. 3. The attempt at a solution Since, you only have 1min. 15s for every problem on the test, usually these problems can be solved in that length of time. So, I am trying to find a way to get to the correct answer by using reasoning and elimination instead of actually integrating to find the correct coefficients (time consuming). Here is where I am at: You can eliminate all choices except for A and B since the terms in the series must be odd functions since the function we are expanding is odd. Now, I can't seem to find a good way to narrow the answer down to B, which is the correct answer. Their explanation does not make sense, since if A is trivially 0 then so is B. Does anyone here have any ideas? I have been staring at this for quite some time. Yet, I can't find a good way to eliminate A, except by brute calculation of the series. Any thoughts and help will be appreciated. Thank you.