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Inequality with Equality Condition

Source:

August 8, 2024
inequalitiesalgebra2022

Problem Statement

Find the least positive integer NN such that there exist positive real numbers a1,a2,…,aNa_1,a_2,\dots,a_N such that \sum_{k=1}^{N}ka_k=1   \text{and}   \sum_{k=1}^{N}\frac{a_k^2}{k}\leq \frac{1}{2022^2}.
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