I want to show that $\sum^{\infty}_{n=1}\frac{\sin(nx)}n$ converges uniformly on $[a, 2\pi - a]$ for $0
Actually, I know $\sum^{\infty}_{n=1}\frac{\sin(nx)}n$ converges (by using Dirichlet test).
However, it is difficult for me to prove converge "uniformly".
How can I prove this?
Do I have to use Weierstrass M-test?
Then how?