Sum of the series $\;S=\large\frac{4}{7}-\large\frac{5}{7^2}+\large\frac{4}{7^3}-\large\frac{5}{7^4}+.....\;\infty\;$ is :

Question

$(a)\;\large\frac{4}{43}\qquad(b)\;\large\frac{3}{11}\qquad(c)\;\large\frac{23}{48}\qquad(d)\;\large\frac{23}{24}$