$$ x(k)=4[u(k-2)-u(k)*δ(k-3)]$$
I found that the $\mathcal{Z}$ transform of the signal is $X(z)=4/(z^2)$.
What would the ROC be?
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It only takes a minute to sign up.
Sign up to join this communityHINT:
Remember that the ROC is the region in the $z$-plane for which the series
$$X(z)=\sum_{n=-\infty}^{\infty}x[n]z^{-n}\tag{1}$$
converges. Since you've found $X(z)$ you also know that $x[n]=4\delta[n-2]$, i.e. there's only one value of $n$ for which $x[n]$ is not equal to zero. What does that mean for the convergence of $(1)$?
So the $\mathcal{Z}$ transform is $4z^{-2}$ so that the actual signal is $4\delta[n-2]$. From this table, that means that the ROC is all of $z$ except the origin.
homework
tag. $\endgroup$