The simplified value of ( 1 - 1/3 ) ( 1 - 1/4 ) ( 1 - 1/5 ) . . . . . ( 1 - 1/99 ) ( 1 - 1/100 )

Answer: Option C

$$\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)$$     . . . . .$$\left(1-\frac{1}{99}\right)$$ $$\left(1-\frac{1}{100}\right)$$
$$\begin{array}{rl}& =\frac{2}{3}\times \frac{3}{4}\times \frac{4}{5}\times .....\times \frac{98}{99}\times \frac{99}{100}\\ & =\frac{2}{100}\\ & =\frac{1}{50}\end{array}$$