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
• E. 2

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 $d=\frac{2.5}{1.7}$ which is the correct answer

Option $e=2,$ which can never be the answer