1. The problem statement, all variables and given/known data I am looking for a closed form of the summation: sin(x) + sin(3x) + sin(5x) + ... + sin((2n-1*)x) 2. Relevant equations None. 3. The attempt at a solution Through a complete stroke of luck, I believe I have arrived at the correct solution: sin^2(nx)/sin(x) I have tested this for many different cases, and I believe it is correct. However, I am having a hard time proving that it is. Can anybody point me in the right direction?