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Simplify: \({\left[ {\left( {1 - \;\frac{1}{2}} \right)\left( {1 - \;\frac{1}{3}} \right)\left( {1 - \;\frac{1}{4}} \right)\left( {1 - \;\frac{1}{5}} \right) \ldots \ldots ..\left( {1 - \;\frac{1}{{100}}} \right)} \right]^{ - 0.5}} = \;?\)1. 12. 103. 0.14. 100 |
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Answer» Correct Answer - Option 2 : 10 We are given the following equation: \({\left[ {\left( {1 - \;\frac{1}{2}} \right)\left( {1 - \;\frac{1}{3}} \right)\left( {1 - \;\frac{1}{4}} \right)\left( {1 - \;\frac{1}{5}} \right) \ldots \ldots ..\left( {1 - \;\frac{1}{{100}}} \right)} \right]^{ - 0.5}} = \;?\) ⇒ [(1/2) × (2/3) × (3/4) × (4/5) × .................. × (99/100)]–0.5 = ? In this equation, each denominator of previous term will be cancelled out by the numerator of the next term. Hence, we obtain: ⇒ [1 × (1/100)]–0.5 ⇒ (100)0.5 ⇒ 10 ∴ \({\left[ {\left( {1 - \;\frac{1}{2}} \right)\left( {1 - \;\frac{1}{3}} \right)\left( {1 - \;\frac{1}{4}} \right)\left( {1 - \;\frac{1}{5}} \right) \ldots \ldots ..\left( {1 - \;\frac{1}{{100}}} \right)} \right]^{ - 0.5}} = \;10\) |
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