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Can someone help me with this sum

 
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Feb7-05, 12:44 PM   #1
 

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
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Feb8-05, 01:05 PM   #2
 
sin(nx)/n = RE[e^inx/n]
(Further Hint : log series)

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Feb8-05, 03:33 PM   #3
 
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Correction to TenaliRaman. sin is imaginary part, cos is real part.
Feb8-05, 11:02 PM   #4
 
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Can someone help me with this sum


I would try computing the fourier coefficents of x.
Feb9-05, 07:52 AM   #5
 
Quote by mathman
Correction to TenaliRaman. sin is imaginary part, cos is real part.
OOPS!

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