MathDB

Inequality

Source: Polish National Olympiad 2015 2nd round, 2nd problem

March 3, 2015

inequalities

Problem Statement

Let

A

be an integer and

A>1

. Let

a_{1}=A^{A}

a_{n+1}=A^{a_{n}}

and

b_{1}=A^{A+1}

b_{n+1}=2^{b_{n}}

n=1, 2, 3, ...

. Prove that

a_{n}<b_{n}

for each

n