1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution i'm pretty much learning fourier series from scratch today after only looking at it in lectures (and my exam is tomorrow lol @ me) and i'm sort of stuck. The solutions have something different to what i have, i think it might be an error in their integration by parts (which i also learnt today, despite how simple it seems). this is my working out: http://i.imgur.com/6OXlr.jpg and this is the worked solutions: http://i.imgur.com/1RAJL.png doesnt the integral of (1/n)*sin(nx) equal to (-1/n^2)*cos(nx)? like i have in my working? because the solutions are saying it integrates into (-1/n)*cos(nx). or is mine set out incorrectly after i've integrated by parts? edit: i've only shown both workings from where i had to find a subscript n, before that everything was fine and correct.