[tex] \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} \times \frac{5}{6} \times \frac{6}{7} \times ...... \times \frac{98}{99} \times \frac{99}{100 } = [/tex]​

There's a clear pattern arising from this multiplication: the denominator of a fraction always simplifies with the numerator of the next one.Since every denominator simplifies with every next numerator, the only remaining terms will be the first numerator and the last denominator.Here's an example of the first few steps:[tex]\dfrac{2}{3}\cdot \dfrac{3}{4}=\dfrac{2}{4}[/tex]Since we simplify the 3's. Multiplying the next fraction gives[tex]\dfrac{2}{4}\cdot \dfrac{4}{5}=\dfrac{2}{5}[/tex]Since we simplify the 4's. So on and so forth, we would arrive at the final multiplication[tex]\dfrac{2}{99}\cdot \dfrac{99}{100}=\dfrac{2}{100}=\dfrac{1}{50}[/tex]