A. 713

Part of KoMaL A Problems 2017/2018

Problems(1)

Bounded expansive sequences

Source: KöMaL A. 713

We say that a sequence

a_1,a_2,\cdots

is expansive if for all positive integers

j,\; i<j

|a_i-a_j|\ge \tfrac 1j

. Find all positive real numbers

C

for which one can find an expansive sequence in the interval

[0,C]

algebraSequencepositive