2022 AMC 8 Problem 8 - Math Gold Medalist

Lor

2022 AMC 8

Problem 8

What is the value of $\frac{1}{3}\cdot\frac{2}{4}\cdot\frac{3}{5}\cdots\frac{18}{20}\cdot\frac{19}{21}\cdot\frac{20}{22}?$

$\textbf{(A) } \frac{1}{462} \qquad \textbf{(B) } \frac{1}{231} \qquad \textbf{(C) } \frac{1}{132} \qquad \textbf{(D) } \frac{2}{213} \qquad \textbf{(E) } \frac{1}{22}$

Related Ideas

Telescoping Rule/Product

Hint

Numerators will be cancelled from 3 and denominators will be cancelled up to 20