Sum of sin(nx)/n from 1 to infinity

[Bossieman]

sum (sin(nx)/n)
where n goes from 1 to infinity.
The result should be (1/2)*(pi-x) when 0(x(pi
and -(1/2)*(pi+x) when -pi(x(0

I need someone to show me how to attack this problem.
Thanks

 

[TenaliRaman]

sin(nx)/n = RE[e^inx/n]
(Further Hint : log series)

-- AI

 

[mathman]

Correction to TenaliRaman. sin is imaginary part, cos is real part.

 

[mathwonk]

I would try computing the Fourier coefficents of x.

 

[TenaliRaman]

Correction to TenaliRaman. sin is imaginary part, cos is real part.

OOPS!

-- AI