1. **Problem:** Find the Z-transform $Z(n)$. 2. **Formula and explanation:** The Z-transform of a sequence $x_n$ is defined as $$Z\{x_n\} = X(z) = \sum_{n=0}^\infty x_n z^{-n}.$$ 3. **Step-by-step solution:** - The problem asks for $Z(n)$, which is ambiguous but usually means the Z-transform of the sequence $x_n = n$. - The Z-transform of $x_n = n$ is known to be $$X(z) = \frac{z}{(z-1)^2}$$ for $|z| > 1$. 4. **Explanation:** - This comes from the formula for the Z-transform of $n$: $$Z\{n\} = z \frac{d}{dz} \left( \frac{1}{1 - z^{-1}} \right) = \frac{z}{(z-1)^2}.$$ 5. **Answer:** Option A: $\frac{z}{(z-1)^2}$. Final answer: $Z(n) = \frac{z}{(z-1)^2}$.