Please see the attached file for the fully formatted problem.
Let Y: R --> R be the periodic function whose restriction to [0,1] is X (0,1/2) - X(1/2,1)
Y is an odd function.
S 1--> 0 Y(x) cos 2pi kx dx = S 1/2-->-1/2 Y(x) cos 2pi kx dx Vk
Conclude the the complex Fourier Series...can be expressed in the form... and compute the bk's.
A problem involving complex Fourier series is solved. The solution is detailed and well presented.