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The $Z$-transform of the time function $\sum_{k=0}^{\infty} \delta(n-k)$ is

  1. $\frac{Z-1}{Z}$
  2. $\frac{Z}{Z-1}$
  3. $\frac{Z}{(Z-1)^2}$
  4. $\frac{(Z-1)^2}{Z}$
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