Extra Credit Problem$)(30$ Points$)$

Given an LTI system described by:

$H(z)=\frac{Y(z)}{x(z)}=\frac{z}{z-0\mathrm{.}5}$ and ROC:$|z|>0\mathrm{.}5$

a$)$ Find the unit step response, $x[n]=u[n].$

b$)$ Find the unit ramp response, $x[n]=$

$u[n].$