1950 AHSME Problems/Problem 43

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Problem

The sum to infinity of $\frac{1}{7}\plus{}\frac {2}{7^2}\plus{}\frac{1}{7^3}\plus{}\frac{2}{7^4}\plus{}...$ (Error compiling LaTeX. Unknown error_msg) is:

$\textbf{(A)}\ \frac{1}{5} \qquad \textbf{(B)}\ \dfrac{1}{24} \qquad \textbf{(C)}\ \dfrac{5}{48} \qquad \textbf{(D)}\ \dfrac{1}{16} \qquad \textbf{(E)}\ \text{None of these}$