Let $S=\frac{3}{19}+\frac{33}{(19)^2}+\frac{333}{(19)^3}+$......$\infty$. Find $S$.

Question

$(a)\;\frac{19}{54}\qquad(b)\;\frac{3}{19}\qquad(c)\;\frac{27}{171}\qquad(d)\;None$