Evaluate the continued fraction: x=2+{1}{3+{1}{4+1/2}}

Correct Answer is : (67)/(29)(67)/(29)(67)/(29)

Evaluate the continued fraction: x=2+{1}{3+{1}{4+1/2}}

Correct Answer is : (67)/(29)(67)/(29)(67)/(29)

Test Index

SSC CGL Tier I 12 Sep 2025 Shift 2 Paper

Question : 53 of 100

Marks: +1, -0

x=2+\frac{1}{3+\frac{1}{4+\frac{1}{2}}}

$(67)/(29)$
$(41)/(17 )$
$(45)/(19)$
$(47)/(20)$

Validate

Solution:

Concept:

A continued fraction is simplified from the innermost part outward. First simplify the deepest fraction, then work step by step to the outermost level.

Explanation:

Start with the innermost fraction:

4+\frac{1}{2} = \frac{9}{2}

Its reciprocal is

\frac{2}{9}

, so

3+\frac{1}{4+\frac{1}{2}} = 3+\frac{2}{9} = \frac{29}{9}

The reciprocal of

\frac{29}{9}

\frac{9}{29}

. Then

x = 2 + \frac{9}{29} = \frac{58}{29} + \frac{9}{29} = \frac{67}{29}

Answer:

Option A:

\frac{67}{29}

Go to Question:

Prev Question

Next Question