MathDB

Bounded Sequences

Source: IZhO 2022 Day 2 Problem 6

February 18, 2022

algebraSequencecombinatoricsizho

Problem Statement

Do there exist two bounded sequences

a_1, a_2,\ldots

and

b_1, b_2,\ldots

such that for each positive integers

n

and

m>n

at least one of the two inequalities

|a_m-a_n|>1/\sqrt{n},

and

|b_m-b_n|>1/\sqrt{n}

holds?

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