Question

If $x=\frac{1}{2},$ then the value of $x+\frac{1}{1+\frac{1}{1+\frac{1}{x}}}$ is

• A. $\frac{5}{4}$
• B. $\frac{4}{5}$
• C. $\frac{3}{4}$
• D. None of these

Answer 1

The correct option is A $\frac{5}{4}$

if $x=\frac{1}{2}\Rightarrow \frac{1}{x}=2$
Now,
$x+\frac{1}{1+\frac{1}{1+\frac{1}{x}}}=\frac{1}{2}+\frac{1}{1+\frac{1}{1+2}}$
$=\frac{1}{2}+\frac{1}{1+\frac{1}{3}}$
$=\frac{1}{2}+\frac{1}{\frac{4}{3}}$
$=\frac{1}{2}+\frac{3}{4}$
$=\frac{5}{4}$
Option A is correct.