MathDB
Two recursive sequences and an inequality

Source: MEMO 2024 T1

August 27, 2024
Sequencesalgebraalgebra proposedinequalitiesinequalities proposed

Problem Statement

Consider two infinite sequences a0,a1,a2,…a_0,a_1,a_2,\dots and b0,b1,b2,…b_0,b_1,b_2,\dots of real numbers such that a0=0a_0=0, b0=0b_0=0 and a_{k+1}=b_k,   b_{k+1}=\frac{a_kb_k+a_k+1}{b_k+1} for each integer k≥0k \ge 0. Prove that a2024+b2024≥88a_{2024}+b_{2024} \ge 88.
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