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What about :

sage: var("q")
q
sage: f(q)=(q+1)/(q-3);f
q |--> (q + 1)/(q - 3)
sage: f.maxima_methods().powerseries(q,oo)
4*sum(3^(i1 - 1)/q^i1, i1, 0, +Infinity) - 1/3