I am trying to understand Region of Convergence (RoC) of Z-transform.
If $x(n) = a^n u(n)$ then its z-transform is given as
$X(z) = \sum_{-\infty}^{+\infty}x(n) z^{-n} = \sum_{0}^{\infty}a(n) z^{-n}$. This expression can be further written as:
$X(z)= \sum_{0}^{\infty} (az^{-1})^n$ ---(1)
For convergence of $X(z)$, we require that summation in eq.(1) should be lesser than $\infty$, i.e.,
$\sum_{0}^{\infty} (az^{-1})^n < \infty$ ---(2)
I had understood both eq.(1) and eq. (2).
However, in some of the text it is written that "Consequently, RoC is that range of values of $z$ for which $|az^{-1}|< 1$".
My query is that, I am not getting how $|az^{-1}|< 1$ comes into the picture, especially after eq. (2).
Any help in this regard will be highly appreciated.