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The value of \(1 - \frac{1}{{1 - \frac{1}{{1 - \frac{1}{x}}}}}\) is1. \(\frac{1}{x}\)2. x + 13. x4. None of the above |
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Answer» Correct Answer - Option 3 : x Given: \(1 - \frac{1}{{1 - \frac{1}{{1 - \frac{1}{x}}}}}\) Calculations: \(1 - \frac{1}{{1 - \frac{1}{{1 - \frac{1}{x}}}}}\) ⇒ \(1 - \frac{1}{{1 - \frac{1}{{\frac{x - 1}{x}}}}}\) ⇒ \(1 - \frac{1}{{1 - \frac{x}{{{x - 1}{}}}}}\) ⇒ \(1 - \frac{1}{{\frac{x - 1 - x}{{{x - 1 }{}}}}}\) ⇒ \(1 - \frac{x - 1}{{{ -1}{{{}}}}}\) ⇒ 1 + x - 1 ⇒ x ∴ The required value of the given expression is x |
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