Given series $$\sum_{n=1}^{\infty}\frac{\cos(nx)}{2n-1}$$
how can we find the sum of given series?
Update:
This task is from calculus workbook we got in class, so I can't give a valid source where the task came from. I've tried to change $$\cos$$ to $$z^n$$ so I would have a power series and it would be possible to create a geometric progression using it, and then I would find the real part of it. Unfortunately, I can't implement this idea because after that I don't know how to get rid of complex numbers