What will come in place of question mark in the following question?
\(\left( {1 - \frac{1}{2}} \right)\left( {1 - \frac{1}{3}} \right)\left( {1 - \frac{1}{4}} \right)\left( {1 - \frac{1}{5}} \right) \ldots \ldots .\left( {1 - \frac{1}{x}} \right) = ?\)
Solution
Correct Answer: Option C
\(\begin{array}{l} \left( {1 - \frac{1}{2}} \right)\left( {1 - \frac{1}{3}} \right)\left( {1 - \frac{1}{4}} \right)\left( {1 - \frac{1}{5}} \right) \ldots \ldots .\left( {1 - \frac{1}{x}} \right) = ?\\ \Rightarrow ? = \left( {1 - \frac{1}{2}} \right)\left( {1 - \frac{1}{3}} \right)\left( {1 - \frac{1}{4}} \right)\left( {1 - \frac{1}{5}} \right) \ldots \ldots .\left( {1 - \frac{1}{{x - 1}}} \right)\left( {1 - \frac{1}{x}} \right)\\ \Rightarrow ? = \frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} \times \ldots \ldots . \times \left( {\frac{{x - 2}}{{x - 1}}} \right)\left( {\frac{{x - 1}}{x}} \right) \end{array}\)
⇒ ? = 1/x
Hence, the required answer is (1/x)
Practice More Questions on Our App!
Download our app for free and access thousands of MCQ questions with detailed solutions