AHSME 1951 Problem 11

The limit of the sum of an infinite number of terms in a geometric progression is $\frac {a}{1 - r}$ where $a$ denotes the first term and $- 1 < r < 1$ denotes the common ratio. The limit of the sum of their squares is: $\textbf{(A)}\ \frac {a^2}{(1 - r)^2} \textbf{(B)}\ \frac {a^2}{1 + r^2} \textbf{(C)}\ \frac {a^2}{1 - r^2} \textbf{(D)}\ \frac {4a^2}{1 + r^2} \textbf{(E)}\ \text{none of these}$