Consider a signal $x\left [ n \right ]=\left ( \dfrac{1}{2} \right )^{n}1\left [ n \right ],$ where $1\left [ n \right ]=0$ if $n< 0$, and $1\left [ n \right ]= 1$ if $n \geq 0.$ The z-transform of $x\left [ n-k \right ],\:k> 0$ is $\dfrac{z^{-k}}{1-\frac{1}{2}z^{-1}}$ with region of convergence being
- $\mid z \mid< 2$
- $\mid z \mid> 2$
- $\mid z \mid < \dfrac{1}{2}$
- $\mid z \mid > \dfrac{1}{2}$