MathDB

Prove that the sequence has a finite limit

Source: Vietnam NMO 1988 Problem 4

February 2, 2009

inductionalgebra unsolvedalgebra

Problem Statement

A bounded sequence

(x_n)_{n\ge 1}

of real numbers satisfies x_n \plus{} x_{n \plus{} 1} \ge 2x_{n \plus{} 2} for all

n \ge 1

. Prove that this sequence has a finite limit.