Linearity
where the ROC is the region where both 
and 
converge.
Example - the 2-sided exponential sequence
Using linearity and transforms found above :
The ROC is |z|>|a| for the first term and |z|<|b| for the second. Thus there is no ROC unless
|b|>|a| .
Shifting property of the transform
Suppose 
Substitute p=n-m so n=m+p :
Multiplication by n and derivatives in z
