For the given LTI system,

y$($n$)=$y$($n$-1)-0\mathrm{.}5$y$($n$-2)+$x$($n$)+$x$($n$-1)$

$1.$ Determine the impulse response, h$($n$)$ of the system.

$2.$ Determine the step response of the system if x$($n$)=$u$($n$).($ write full answer$).$

$3.$ what is the region of convergence $($ROC$)?($show the steps$).$