If \({\rm{x}}\left[ {\rm{n}} \right] = {\left( {\frac{1}{3}} \right)^{\left| {\rm{n}} \right|}}-{(\frac{1}{2})}^n \ u(n) \) then, the region of convergence of its z transform in the z-plane will be
1
\( \frac{1}{3}<\left| z \right| < 3\)
2
\( \frac{1}{2}<\left| z \right| < 3\)
3
\( \frac{1}{3}<\left| z \right| < \frac{1}{2}\)
4
\( \frac{1}{3}<\left| z \right| \)