MathDB

1

Part of 2024 Benelux

Problems(1)

2024 BxMO P1

Source: 2024 BxMO P1

4/27/2024
Let a0,a1,…,a2024a_0,a_1,\dots,a_{2024} be real numbers such that ∣ai+1−ai∣≤1\left|a_{i+1}-a_i\right| \le 1 for i=0,1,…,2023i=0,1,\dots,2023. a) Find the minimum possible value of a0a1+a1a2+⋯+a2023a2024a_0a_1+a_1a_2+\dots+a_{2023}a_{2024} b) Does there exist a real number CC such that a0a1−a1a2+a2a3−a3a4+⋯+a2022a2023−a2023a2024≥Ca_0a_1-a_1a_2+a_2a_3-a_3a_4+\dots+a_{2022}a_{2023}-a_{2023}a_{2024} \ge C for all real numbers a0,a1,…,a2024a_0,a_1,\dots,a_2024 such that ∣ai+1−ai∣≤1\left|a_{i+1}-a_i\right| \le 1 for i=0,1,…,2023i=0,1,\dots,2023.
Algebra inequalitySequencesalgebrainequalities