Question

Solve for x.
$x=1+\frac{1}{3+\frac{1}{2+\frac{1}{3+\frac{1}{2+....\infty }}}}$

• A. 50/17
• B. 10/17
• C. 30/14
• D. 25/17

Answer 1

The correct option is D 25/17

$1+\frac{1}{3}=\frac{4}{3}=\mathrm{1.333.}$ The value of x will be slightly lesser than $1.333$ as the denominator keeps increasing.

Look at the options -

Option $a=\frac{5}{1.7}>2$. This can never be the answer.

Option $b=\frac{1}{1.7}<1$. This also can never be the answer.

Option $c=\frac{3}{1.4}>2$. This cannot be the answer.

Option $d=\frac{2.2}{1.7}\approx 1.29$ which is the correct answer.