Question

The value of following fraction is:
$3+\frac{1}{3+\frac{1}{3+\frac{1}{3}}}$

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is B

$3+\frac{1}{3+\frac{1}{3+\frac{1}{3}}}$
$=3+\frac{1}{3+\frac{1}{\frac{9+1}{3}}}$
$=3+\frac{1}{3+\frac{1}{\frac{10}{3}}}$
$=3+\frac{1}{3+\frac{3}{10}}$
$=3+\frac{1}{\frac{30+3}{10}}$
$=3+\frac{1}{\frac{33}{10}}$
$=3+\frac{10}{33}$
$=\frac{99+10}{33}$
$=\frac{109}{33}$