Question: Can maple compute it faster?

How do I evaluate moments of Q4 in a reasonable time with a reasonable accuracy, i.e. to a few decimal points:
with(Statistics): RV := 'RandomVariable(Geometric(1/3))+1'; R := `$`('RV', 5);

Q4 := 1/(alpha*R[1]+alpha^2*R[2]+alpha^3*R[3]+(1-alpha-alpha^2-alpha^3)*R[4]);

Moment(Q4, 1);

E.g., can I tell maple that replacing infinite series underlying this calculation with sufficiently long partial sums is okay with me? Or maybe there is a theoretically sound approxmation to avoid calculating the reciprocal moments of convex combinations directly. Or maybe there is a clever speed-up to compute the exact values..?


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