MathDB
Harmonic progression

Source: 1959 AMC 12 Problem 33

August 14, 2013
AMCharmonic progressionarithmetic seriesarithmetic sequencealgebraAMC 12

Problem Statement

A harmonic progression is a sequence of numbers such that their reciprocals are in arithmetic progression. Let SnS_n represent the sum of the first nn terms of the harmonic progression; for example S3S_3 represents the sum of the first three terms. If the first three terms of a harmonic progression are 3,4,63,4,6, then: <spanclass=latexbold>(A)</span> S4=20<spanclass=latexbold>(B)</span> S4=25<spanclass=latexbold>(C)</span> S5=49<spanclass=latexbold>(D)</span> S6=49<spanclass=latexbold>(E)</span> S2=12S4 <span class='latex-bold'>(A)</span>\ S_4=20 \qquad<span class='latex-bold'>(B)</span>\ S_4=25\qquad<span class='latex-bold'>(C)</span>\ S_5=49\qquad<span class='latex-bold'>(D)</span>\ S_6=49\qquad<span class='latex-bold'>(E)</span>\ S_2=\frac12 S_4