MathDB
Bounded sequence !!

Source: Romania TST 2015 Day 3 Problem 2

June 4, 2015
boundedSequencesRecurrencealgebraRomanian TST

Problem Statement

Let (an)n≥0(a_n)_{n \geq 0} and (bn)n≥0(b_n)_{n \geq 0} be sequences of real numbers such that a0>12 a_0>\frac{1}{2} , an+1≥ana_{n+1} \geq a_n and bn+1=an(bn+bn+2)b_{n+1}=a_n(b_n+b_{n+2}) for all non-negative integers nn . Show that the sequence (bn)n≥0(b_n)_{n \geq 0} is bounded .
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