# Can someone help me with this sum

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

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

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

mathwonk
Homework Helper
2020 Award
I would try computing the fourier coefficents of x.

mathman said:
Correction to TenaliRaman. sin is imaginary part, cos is real part.
OOPS!

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