If $$x\left[ n \right] = {\left( {{1 \over 3}} \right)^{\left| n \right|}} - {\left( {{1 \over 2}} \right)^n}u\left[ n \right],$$     then the region of convergence (ROC) of its z-transform in the z-plane will be

A. $${1 \over 3} < \left| z \right| < 3$$

B. $${1 \over 3} < \left| z \right| < {1 \over 2}$$

C. $${1 \over 2} < \left| z \right| < 3$$

D. $${1 \over 3} < \left| z \right|$$

Answer: Option C