1959 AHSME Problem 33

A harmonic progression is a sequence of numbers such that their reciprocals are in arithmetic progression. Let S_n represent the sum of the first n terms of the harmonic progression; for example S_3 represents the sum of the first three terms. If the first three terms of a harmonic progression are 3,4,6, then: \textbf{(A)}\ S_4=20 \qquad\textbf{(B)}\ S_4=25\qquad\textbf{(C)}\ S_5=49\qquad\textbf{(D)}\ S_6=49\qquad\textbf{(E)}\ S_2=\frac{1}2 S_4

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