AHSME 1950 Problem 43

The sum to infinity of $\frac{1}{7}+\frac {2}{7^2}+\frac{1}{7^3}+\frac{2}{7^4}+\cdots$ is: $\textbf{(A)}\ \frac{1}{5} \textbf{(B)}\ \dfrac{1}{24} \textbf{(C)}\ \dfrac{5}{48} \textbf{(D)}\ \dfrac{1}{16} \textbf{(E)}\ \text{None of these}$