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The value of \(\left( {1 - \frac{1}{2}} \right)\left( {1 - \frac{1}{3}} \right)\left( {1 - \frac{1}{4}} \right)......\left( {1 - \frac{1}{{40}}} \right)\) on simplification is

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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

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