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. none of these

Answer 1

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

Given: $x=\frac{1}{2}$

$\therefore \frac{1}{x}=\frac{2}{1}=2$
So, $1+\frac{1}{x}=1+2=3$

Now, $x+\frac{1}{1+\frac{1}{1+\frac{1}{x}}}$

$=x+\frac{1}{1+\frac{1}{3}}$ [Putting the value of $1+\frac{1}{x}=3$]

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

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

$=\frac{5}{4}$