Question

Simplify $(1-\frac{1}{3})(1-\frac{1}{4})(1-\frac{1}{5})\dots \dots .(1-\frac{1}{100})$

Answer 1

Given $(1-\frac{1}{3})(1-\frac{1}{4})(1-\frac{1}{5})\dots \dots .(1-\frac{1}{100})$

$\frac{2}{3}\times \frac{3}{4}\times \frac{4}{5}\times \frac{5}{6}\times \dots \dots \frac{98}{99}\times \frac{99}{100}$

$\Rightarrow \frac{2}{100}=\frac{1}{50}$.