Question: Having problem with infinite series

I tried Maple to find a closed-form expression of the following infinite
where r and a are probabilities and |z|<1.
It did not work
Then I tried to get a series expansion of F around z=0, i.e:
Got the following error message:
Error, (in series/exp) unable to compute series
However when the upper limit of the summation is changed from infinity to any pre-defined number;
ex: F:=sum(r^j/(1-a*z^j),j=1..100)
Maple was able to derive the series expansion around z=0.
Is there any way to get the series expansion at z=0, when the upper limit of the summation is infinity ?
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