Correct Answer - Option 4 :
\(\frac{1}{{40}}\)
Given:
\(\left( {1 - \frac{1}{2}} \right)\left( {1 - \frac{1}{3}} \right)\left( {1 - \frac{1}{4}} \right)......\left( {1 - \frac{1}{{40}}} \right)\)
Calculations:
\(\left( {1 - \frac{1}{2}} \right)\left( {1 - \frac{1}{3}} \right)\left( {1 - \frac{1}{4}} \right)......\left( {1 - \frac{1}{{40}}} \right)\) = [(2 -1)/2][(3 - 1)/3][(4 - 1)/4] ......[(39 - 1)/39][(40 -1)/40]
⇒ (1/2)(2/3)(3/4) . . . . . . (38/39)(39/40) = 1/40
∴ The required value is 1/40