1962 AHSME Problem 14

Let s be the limiting sum of the geometric series 4- \frac{8}{3} + \frac{16}{9} - \ldots , as the number of terms increases without bound. Then s equals:

\textbf{(A)}\ \text{a number between 0 and 1} \qquad \textbf{(B)}\ 2.4 \qquad \textbf{(C)}\ 2.5 \qquad \textbf{(D)}\ 3.6\qquad \textbf{(E)}\ 12

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