Question

If \(x = \frac{1}{2}\), then the value of \(x + \frac{1}{{1 + \frac{1}{{1 + \frac{1}{x}}}}}\) will be

[UTET Sept 2013]

1. \(\frac{5}{4}\)
2. \(\frac{4}{5}\)
3. \(\frac{3}{4}\)
4. \(\frac{11}{10}\)

Answer 1

Correct Answer - Option 1 : \(\frac{5}{4}\)

\(x + \frac{1}{{1 + \frac{1}{{1 + \frac{1}{x}}}}} = \frac{1}{2} + \frac{1}{{1 + \frac{1}{{1 + 2}}}}\)

\(= \frac{1}{2} + \frac{1}{{\frac{4}{3}}} = \frac{1}{2} + \frac{3}{4} = \frac{5}{4}\)