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4

Part of 1999 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

sum 1/ \sqrt[3]{1^2}+\sqrt[3]{1 x 2}+\sqrt[3]{2^2} } + ...>9/2

Source: Rioplatense 1999 L3 P4

9/19/2022
Prove the following inequality: 1123+1⋅23+223+1323+3⋅43+423+...+199923+999⋅10003+100023>92 \frac{1}{\sqrt[3]{1^2}+\sqrt[3]{1 \cdot 2}+\sqrt[3]{2^2} }+\frac{1}{\sqrt[3]{3^2}+\sqrt[3]{3 \cdot 4}+\sqrt[3]{4^2} }+...+ \frac{1}{\sqrt[3]{999^2}+\sqrt[3]{999 \cdot 1000}+\sqrt[3]{1000^2} }> \frac{9}{2}
(The member on the left has 500 fractions.)
inequalitiesalgebra