this is going to be a long one:
so:
now we have to evaluate the series at t=0:
now we'll play a little with the sum:
thus:
Q.E.D.
Define on and extend f to be -periodic.
By evaluating the Fourier series for t = 0, show that;
So for the first part, extending f to be -periodic gives , for i think.
Then evaluating t at 0... well i couldnt make the last two fourier lectures so im a bit lost here.