MathDB

7

Part of 2023 Thailand Online MO

Problems(1)

minimum of two consecutive terms is less than 1

Source: 2023 Thailand Online MO P7

2/12/2023
Let a0,a1,…a_0,a_1,\dots be a sequence of positive reals such that an+2≤2023ananan+1+2023 a_{n+2} \leq \frac{2023a_n}{a_na_{n+1}+2023} for all integers n≥0n\geq 0. Prove that either a2023<1a_{2023}<1 or a2024<1a_{2024}<1.
Inequalityalgebra