If the above series converges it can be considered as a geometric series
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converges when
IaI < 1
i.e. IzI > 2
Thus the convergence
depends on the magnitude of z. The z transform is
therefore specified by its expression and
region of convergence.
Consider the same expression and change ROC as
IzI < 2, and we get a different sequence
Therefore , the given expression is
the z transform of 
Thus a z-transform is incomplete
without specifying the ROC
