Fourier Series of the Square Wave and the Sinc Function

One period of a square wave $x(t)$ is given by $x(t)=\left\{\begin{array}{cl} 1,&|t|\le 5\\0,&5< |t|\le 20 \end{array}\right.$. Identify the Fourier series coefficients $X[k]$.

If $x(t)=10$ sinc$(20t)$, what is $x(0)$ ?

The size of the peak ripple associated with Gibbs’ phenomena decreases proportional to $1/J$ for a $J$ harmonic Fourier series approximation to the square wave.

One period of a square wave $x(t)$ is given by $x(t)=\left\{\begin{array}{cl}1,&|t|\le \alpha\\0,&\alpha< |t|\le\beta \end{array}\right.$. What happens to the Fourier Series coefficient $X[0]$ as $\alpha/\beta$ decreases?