Question

1
.
1+
is equal to
1 +
1
1
1+
3​

Answer 1

$1 + \dfrac{1}{1 + \dfrac{1}{ \left( 1 + \frac{1}{3} \right) } }$

$= 1 + \dfrac{1}{1 + \dfrac{1}{ \frac{3 + 1}{3} } } = 1 + \dfrac{1}{ \left( 1 + \frac{3}{4} \right)}$

$= 1 + \dfrac{1}{ \frac{4 + 3}{4} } = 1 + \dfrac{4}{7}$

$= \dfrac{7 + 4}{7} = \boxed{ \dfrac{11}{4} }$