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Harmonic series of positive integers

Source: ISI Entrance 2015

May 10, 2015

number theoryalgebra

Problem Statement

Let

m_1< m_2 < \ldots m_{k-1}< m_k

k

distinct positive integers such that their reciprocals are in arithmetic progression.
1.Show that

k< m_1 + 2

. 2. Give an example of such a sequence of length

k

for any positive integer

k