Small but pressing Fourier series question

[toneboy1]

Homework Statement

Please see picture attached

Homework Equations

The Attempt at a Solution

c_k = 1/T ∫ ^a_-a x(t).e^-jk2pit/T

So x(t) = Ʃ_k=-∞^∞ (sin(k.a.2pi/T).^a_-a e^-jk2pit/T)/k.pi

but is is supposed to be:

So x(t) = Ʃ_k=-∞^∞ (sin(k.a.2pi/T).^a_-a e^-jk2pit/T)/k.pi.2.a

but I don't know why?

Thanks

 

[toneboy1]

Sorry, nevermind, I think the pulse height must be 1/2a, not 1 like I thought.

But I just found another related problem I'm struggling with if anyone's interested:
https://www.physicsforums.com/showthread.php?t=654597