QuestionGiven the piecewise function:
\[ f(x) = \begin{cases} 1, & 0 < x < \frac{3}{2}, \\ -1, & \frac{3}{2} < x < 3 \end{cases}$
with period $l = 3$.
Find the Fourier series expansion of the function $f(x)$.
The Fourier series expansion is given by:
$f(x) = \frac{4}{\pi} \sum_{n=0}^{\infty}(-1)^{n} \frac{\cos ((2n+1) \pi x / 3)}{2n+1}.$