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R < 1/15 < S, R=/2 x 3/4 x 5/6 x ...x 223/ 224

Source: 2021 Francophone MO Juniors p1

April 3, 2021
algebrainequalitiesFrancophone

Problem Statement

Let RR and SS be the numbers defined by R=12×34×56×⋯×223224 and S=23×45×67×⋯×224225.R = \dfrac{1}{2} \times \dfrac{3}{4} \times \dfrac{5}{6} \times \cdots \times \dfrac{223}{224} \text{ and } S = \dfrac{2}{3} \times \dfrac{4}{5} \times \dfrac{6}{7} \times \cdots \times \dfrac{224}{225}.Prove that R<115<SR < \dfrac{1}{15} < S.
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