I [Signal and system] Function with fourier series a[k] = 1

[Duke Le]

We have:
Period T = 4, so fundamental frequency w0 = pi/2.
This question seems sooo easy. But when I use the integral:

x(t) = Σa[k] * exp(i*k*pi/2*t).
I get 1 + sum(cos(k*pi/2*t)), which does not converge.

Where did I went wrong ?
Thanks a lot for your help.

 

[BvU]

Hello Duke,

We have T = 4, so w0 = pi/2.

I have no idea what your T and w0 stand for. Especially T. Have you heard of the dirac delta function ? Familiar with distributions ?

 

[Duke Le]

Hello Duke,
I have no idea what your T and w0 stand for. Especially T. Have you heard of the dirac delta function ? Familiar with distributions ?

Thanks for replying! I edited the post. So the answer for this question is:
y(t) = ∑(delta(t - 4k))
From y(t) i can show that a[k] = 1 for all k. But I couldn't find y(t) given that a[k] = 1 since it didn't converge.