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If $x[n]=(1/3)^{|n|}-(1/2)^nu[n],$ then the region of convergence $\text{(ROC)}$ of its $Z-$transform in the $Z-$plane will be 

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