[tex]\dfrac{1}{4}\cdot \dfrac{2}{5}\cdot \dfrac{3}{6}\cdot _{\dots} \cdot \dfrac{96}{99}\cdot \dfrac{97}{100}=\dfrac{1}{4}\cdot \dfrac{2}{5}\cdot\dfrac{3}{6}\cdot\dfrac{4}{7}\cdot\dfrac{5}{8}\cdot\dfrac{6}{9}\cdot\dfrac{7}{10}\cdot_{\dots}\cdot \dfrac{94}{97}\cdot\dfrac{95}{98}\cdot\dfrac{96}{99}\cdot\dfrac{97}{100}=\\ \\ \\ =1\cdot 2\cdot 3\cdot \dfrac{1}{98\cdot 99\cdot 100}=\dfrac{1}{161700}[/tex]
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[tex]\dfrac{1}{4}\cdot \dfrac{2}{5}\cdot \dfrac{3}{6}\cdot _{\dots} \cdot \dfrac{96}{99}\cdot \dfrac{97}{100}=\dfrac{1}{4}\cdot \dfrac{2}{5}\cdot\dfrac{3}{6}\cdot\dfrac{4}{7}\cdot\dfrac{5}{8}\cdot\dfrac{6}{9}\cdot\dfrac{7}{10}\cdot_{\dots}\cdot \dfrac{94}{97}\cdot\dfrac{95}{98}\cdot\dfrac{96}{99}\cdot\dfrac{97}{100}=\\ \\ \\ =1\cdot 2\cdot 3\cdot \dfrac{1}{98\cdot 99\cdot 100}=\dfrac{1}{161700}[/tex]