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Minimum possible value

Source: BdMO 2024 Secondary National P6 Higher Secondary National P3

March 18, 2024
inequalitiesalgebrapermutation

Problem Statement

Let a1,a2,…,a2024a_1, a_2, \ldots, a_{2024} be a permutation of 1,2,…,20241, 2, \ldots, 2024. Find the minimum possible value of∑i=12023[(ai+ai+1)(1ai+1ai+1)+1aiai+1]\sum_{i=1} ^{2023} \Big[(a_i+a_{i+1})\Big(\frac{1}{a_i}+\frac{1}{a_{i+1}}\Big)+\frac{1}{a_ia_{i+1}}\Big]
Proposed by Md. Ashraful Islam Fahim
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