Hi. Well, I have to demonstrate that

Using a previous result of a Fourier series for f(t)=1 if 0<t<1, f(t)=0 if -1<t<0.

I've found that:

I think this result, the series expansion for the function is right. But when I've tried to demonstrate what the problem asks me I get to an absurd, so I'm not sure where the error is.

This is what I did:

Working from here:

So, I'm doing something wrong. Perhaps you can see more clearly where am I committing the mistake.