The simplified value of $$\left( {1 - \frac{1}{3}} \right)$$ $$\left( {1 - \frac{1}{4}} \right)$$ $$\left( {1 - \frac{1}{5}} \right)$$ . . . . .$$\left( {1 - \frac{1}{99}} \right)$$ $$\left( {1 - \frac{1}{100}} \right)$$

A. $$\frac{2}{{99}}$$

B. $$\frac{1}{{25}}$$

C. $$\frac{1}{{50}}$$

D. $$\frac{1}{{100}}$$

Answer: Option C

Solution(By Examveda Team)

$$\left( {1 - \frac{1}{3}} \right)\left( {1 - \frac{1}{4}} \right)\left( {1 - \frac{1}{5}} \right)$$     . . . . .$$\left( {1 - \frac{1}{{99}}} \right)$$ $$\left( {1 - \frac{1}{{100}}} \right)$$
$$\eqalign{ & = \frac{2}{3} \times \frac{3}{4} \times \frac{4}{5} \times ..... \times \frac{{98}}{{99}} \times \frac{{99}}{{100}} \cr & = \frac{2}{{100}} \cr & = \frac{1}{{50}} \cr} $$