Implementing Unilateral Z-Transform of a^n

Hello everyone, I wrote the following lines to implement the unilateral Z-transform of a^n:

close all
clear all
syms n a z
assume(a>0)
S=symsum(a^n*z^-n,n,0,+Inf)

the result is:

piecewise([a == z, Inf], [a ~= z, -(z - z*limit(a^n/z^n, n == Inf))/(a - z)])

The result should be z/(z-a). How can I get it?

Thank you in advance.

Answer 1

[Star Strider]

It is necessary to add assumptions, then a simplify call:

syms a n z 
assume(a > 0)
assumeAlso(a < 1)
assumeAlso(a < z)
S = symsum((a/z)^n, n, 0, Inf);
S = simplify(S, 'Steps',20)

S = 
-z/(a - z)