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Consider a signal $x[n]=\left(\frac{1}{2}\right)^{n} 1[n]$, where $1[n]= 0$ if $n< 0$, and $1[n]= 1$ if $n\geq0$. The z-transform of $x[n-k],k> 0$ is $\dfrac{z^{-k}}{1-\frac{1}{2}z^{-1}}$ with region of convergence being

1. $\mid z \mid < 2$
2. $\mid z \mid > 2$
3. $\mid z \mid < \frac{1}{2}$
4. $\mid z \mid > \frac{1}{2}$
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