\[ \begin{array}{|c|c|} \hline f(t) & \mathcal{Z}[f](z) \\\hline f(t) & \sum_{k=0}^\infty f(k)z^{-k} \\\hline f(k)=1\;(k\geq 0) & \frac{z}{z-1}\;(|z|>1) \\\hline a^k & \frac{z}{z-a}\;(|z|>|a|) \\\hline f(k)=\begin{cases} 1& k=0\\ 0& k\geq …