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Question: Having problem with infinite series

Question:Having problem with infinite series

Maan 0 Maple
series
May 07 2006
0
I tried Maple to find a closed-form expression of the following infinite
series:
F:=sum(r^j/(1-a*z^j),j=1..infinity)
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:
G:=series(F,z=0);
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 ?
Thanx!
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