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Inequality with cubic roots

Source: Tuymaada 2023 Senior P3

July 7, 2023
algebra

Problem Statement

Prove that for every positive integer n≥2n \geq 2, ∑1≤i≤nin+13n≤∑1≤i≤n−1in3n−1.\frac{\sum_{1\leq i \leq n} \sqrt[3]{\frac{i}{n+1}}}{n} \leq \frac{\sum_{1\leq i \leq n-1} \sqrt[3]{\frac{i}{n}}}{n-1}.
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