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The ROC of Z-transform of the discrete time sequence $\quad x(n)=\left(\frac{1}{3}\right)^{n} u(n)-\left(\frac{1}{2}\right)^{n} u(-n-1) \quad$ is

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