What is the Laplace transform $F(s)$ of the signal $f(t), t \geq 0$ defined below? In $t \in[0,1),$
\[f(t)=\left\{\begin{array}{ll}
1, & t \in\left[0, \frac{1}{2}\right) \\
0, & t \in\left[\frac{1}{2}, 1\right)
\end{array}\right.\]
and in $t \geq 1, f(t)=f(t-n), \quad n \leq t < n + 1. \quad n = 1, 2, 3, \dots$
- $\frac{1-e^{-s / 2}}{s}$
- $\frac{1+e^{-s / 2}}{s}$
- $\frac{1}{s\left(1-e^{-s}\right)}$
- $\frac{1}{s\left(1-e^{-s / 2}\right)}$
- $\frac{1}{s\left(1+e^{-s / 2}\right)}$
