Simplify@Sum[(((((1-q))^k)(x^k))/(1-(q^k))), {k,1,n}]

Sum[(((((1-q))^k)(x^k))/(1-q)), {k,1,n}]

Simplify@Sum[(((((1-q))^k)(x^k))/(1-(q^k))), {k,1,∞}]