OFM 2021 J1

Let $R$ and $S$ be the numbers defined by $$R = \dfrac{1}{2} \times \dfrac{3}{4} \times \dfrac{5}{6} \times \cdots \times \dfrac{223}{224} \text{ and } S = \dfrac{2}{3} \times \dfrac{4}{5} \times \dfrac{6}{7} \times \cdots \times \dfrac{224}{225}.$$Prove that $R < \dfrac{1}{15} < S$ .