1967 AHSME Problems/Problem 20

Problem

A circle is inscribed in a square of side $m$ , then a square is inscribed in that circle, then a circle is inscribed in the latter square, and so on. If $S_n$ is the sum of the areas of the first $n$ circles so inscribed, then, as $n$ grows beyond all bounds, $S_n$ approaches:

$\textbf{(A)}\ \frac{\pi m^2}{2}\qquad \textbf{(B)}\ \frac{3\pi m^2}{8}\qquad \textbf{(C)}\ \frac{\pi m^2}{3}\qquad \textbf{(D)}\ \frac{\pi m^2}{4}\qquad \textbf{(E)}\ \frac{\pi m^2}{8}$

Solution

$\fbox{A}$

1967 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 19	Followed by Problem 21
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1967 AHSME Problems/Problem 20

Problem

Solution

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