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Consider a signal $x\left [ n \right ]=\left ( \frac{1}{2} \right )^{n}1\left [ n \right ],$ where $1\left [ n \right ]=0$ if $n< 0$, and $1\left [ n \right ]= 1$ if

$n \geq 0.$ The z-transform of $x\left [ n-k \right ],\:k> 0\:is\:\frac{z^{-k}}{1-\frac{1}{2}z^{-1}}$ with region of convergence being

  1. $\left | z \right |< 2$
  2. $\left | z \right |> 2$
  3. $\left | z \right |< \frac{1}{2}$
  4. $\left | z \right |> \frac{1}{2}$
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