1

Part of 2015 ISI Entrance Examination

Problems(1)

Harmonic series of positive integers

Source: ISI Entrance 2015

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

number theoryalgebra