Editing Z-transform (section)

===Example 1 (no ROC)===
Let <math>x[n] = (.5)^n\ . </math> Expanding <math>x[n]</math> on the interval <math>(-\infty, \infty)</math> it becomes

:<math>x[n] = \left \{\dots, (.5)^{-3}, (.5)^{-2}, (.5)^{-1}, 1, (.5), (.5)^2, (.5)^3, \dots \right \} = \left \{\dots, 2^3, 2^2, 2, 1, (.5), (.5)^2, (.5)^3, \dots \right\}.</math>

Looking at the sum

:<math>\sum_{n=-\infty}^{\infty}x[n]z^{-n} \to \infty.</math>

Therefore, there are no values of <math>z</math> that satisfy this condition.