# RoC of Z transform of signal consisting of 3 values

Let's consider the signal $$x[n]=\{x[1],x[2],x[3]\}$$

It's $$\mathcal{Z}$$ transform is $$\frac {x[1]}{z}+\frac {x[2]}{z^2}+\frac {x[3]}{z^3}$$

My textbook says it converges for all values of $$z$$ but there is a pole at $$z=0$$, so which one is true?

When we speak about convergenge in all the $$Z$$ plane, the points $$z=0$$ and $$z=\infty$$ are not considered.