When simplified the product : $$\left( {2 - \frac{1}{3}} \right)$$ $$\left( {2 - \frac{3}{5}} \right)$$ $$\left( {2 - \frac{5}{7}} \right)$$  .....$$\left( {2 - \frac{{997}}{{999}}} \right)$$

Solution (By Examveda Team)

According to the question,
$$ \Rightarrow \left( {2 - \frac{1}{3}} \right)\left( {2 - \frac{3}{5}} \right)\left( {2 - \frac{5}{7}} \right).....$$       $$\left( {2 - \frac{{997}}{{999}}} \right)$$
$$\eqalign{ & \Rightarrow \frac{5}{3} \times \frac{7}{5} \times \frac{9}{7}.....\frac{{1001}}{{999}} \cr & \Rightarrow \frac{1}{3} \times 1001 \cr & \Rightarrow \frac{{1001}}{3} \cr} $$