Question

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

• A. $\frac{5}{4}$
• B. $\frac{4}{5}$
• C. $\frac{3}{4}$
• D. $\frac{1}{4}$

Answer 1

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

$x+\frac{1}{1+\frac{1}{1+\frac{1}{x}}}$
$=\frac{1}{2}+\frac{1}{1+\frac{1}{1+\frac{1}{\frac{1}{2}}}}$
$=\frac{1}{2}+\frac{1}{1+\frac{1}{1+2}}$
$=\frac{1}{2}+\frac{1}{1+\frac{1}{3}}$
$=\frac{1}{2}+\frac{1}{\frac{4}{3}}$
$=\frac{1}{2}+\frac{3}{4}$
$=\frac{2+3}{4}=\frac{5}{4}$.