1952 AHSME Problem 43

The diameter of a circle is divided into n equal parts. On each part a semicircle is constructed. As n becomes very large, the sum of the lengths of the arcs of the semicircles approaches a length:

\textbf{(A) } \qquad equal to the semi-circumference of the original circle \textbf{(B) } \qquad equal to the diameter of the original circle \textbf{(C) } \qquad greater than the diameter, but less than the semi-circumference of the original circle \textbf{(D) } \qquad that is infinite \textbf{(E) } greater than the semi-circumference

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