Fourier Coefficient Amplitude: Is Infinity Possible?

[magnifik]

Is it possible to have an infinite value for the amplitude of a Fourier coefficient?

The signal is sin(w₀t) from 0 to T/2. My resulting coefficient formula was
F_n = 2/[4pi(1-n)] + 2/[4pi(1+n)]
so for F₁ i got infinity ... is this possible?
or is coefficient just wrong?

 

[tedbradly]

This solution cannot be correct, because if you add the Fourier components up, you will get infinity multiplied by a sinusoid. Does that reconstruct the original signal in the designated range? No, and it must for such a well-behaved original signal.