1953 AHSME Problem 27

The radius of the first circle is 1 inch, that of the second \frac{1}{2} inch, that of the third \frac{1}{4} inch and so on indefinitely. The sum of the areas of the circles is:

\textbf{(A)}\ \frac{3\pi}{4} \qquad \textbf{(B)}\ 1.3\pi \qquad \textbf{(C)}\ 2\pi \qquad \textbf{(D)}\ \frac{4\pi}{3}\qquad \textbf{(E)}\ \text{none of these}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.