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SSC CGL 2025 PYQ — Question 73

SSC CGL - 15 Sep 2025 - Shift 3 • Quantitative Aptitude • Q73

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Which of the following represents the correct simplified value of the continued fraction: x = 1 + 12+12+12\frac{1}{2 + \frac{1}{2 + \frac{1}{2}}}

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Correct answer: B

Explanation

The correct answer is option 2 i.e. 1712\frac{17}{12}.

x = 1 + 12+12+12\frac{1}{2 + \frac{1}{2 + \frac{1}{2}}}

⇒ x = 1 + 12+152\frac{1}{2 + \frac{1}{\frac{5}{2}}} 

⇒ x = 1 + 12+25\frac{1}{2 + {\frac{2}{5}}} 

⇒ x = 1 + 1125\frac{1}{ {\frac{12}{5}}} 

⇒ x = 1 + 512{ {\frac{5}{12}}} = 1712\frac{17}{12}