Question

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

Answer 1

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

This can be written as

$\Rightarrow \left(\frac{2}{3}\right)\left(\frac{3}{4}\right)\left(\frac{4}{5}\right)...\left(\frac{99}{100}\right)$

On simplifying we get

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

$\Rightarrow (1-\frac{1}{3})(1-\frac{1}{4})(1-\frac{1}{5})....(1-\frac{1}{100})=\frac{1}{50}$