Question

simplify the given question above☝️☝️​

Answer 1

Answer:

109/360

Step-by-step explanation:

To Do :-

$\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{3}}}}}}$

Solution :-

$\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{3}}}}}}$

$=\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{\dfrac{9+1}{3}}}}}$

$=\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{\dfrac{10}{3}}}}}}$

$=\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{3+\dfrac{3}{10}}}}$

$=\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{\dfrac{30+3}{10}}}}$

$=\dfrac{1}{3+\dfrac{1}{3+\dfrac{1}{\dfrac{33}{10}}}}$

$=\dfrac{1}{3+\dfrac{1}{3+\dfrac{10}{{33}}}}$

$=\dfrac{1}{3+\dfrac{1}{\dfrac{99+10}{{33}}}}$

$=\dfrac{1}{3+\dfrac{1}{\dfrac{109}{{33}}}}$

$=\dfrac{1}{3+\dfrac{33}{109}}$

$=\dfrac{1}{\dfrac{327+33}{109}}$

$=\dfrac{1}{\dfrac{360}{109}}$

$=\dfrac{109}{360}$