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 ?

hi, i don't know maple at all and i need to figure out how to solve this sytem of equations that model predator prey systems in maple but i get an error when i modify this code > e1 := diff(x(t),t) = k*x(t) - a*x(t)*y(t); > e2 := diff(y(t),t) = -r*y(t) + b*x(t)*y(t); to fit this equation- dx/dt = 2x(1-x/4) - xy dy/dt = -3y + xy x(0) = 1 y(0) = 1 if anyone has time to tell me what i can do to get the equilibrium points, the solution and the table of values for this system, i would be grateful

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How do i find a background curve to a graph, i have data fitted with a spline and i need to find the background curve