Question

 `1+1/(1+1/(1+1/3))`

Answer 1

`1+1/(1+1/(1+1/3))`

`=1+1/(1+1/(3/3+1/3))`

`=1+1/(1+1/(4/3))`

`=1+1/(1+3/4)`

`=1+1/(4/4+3/4)`

`=1+1/(7/4)`

`=1+4/7`

`=7/7+4/7`

`=11/7`

Answer 2

`1+1/[1+1/[1+1/3]]`

`=1+1/[1+1/[3/3+1/3]]`

`=1+1/[1+1/[4/3]]`

`=1+1/[1+3/4]`

`=1+1/[4/4+3/4]`

`=1+1/[7/4]`

`=1+4/7=7/7+4/7=11/7`

Answer 3

\(1+\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{3}}}=1+\dfrac{1}{1+\dfrac{1}{\dfrac{4}{3}}}=1+\dfrac{1}{1+\dfrac{3}{4}}=1+\dfrac{1}{\dfrac{7}{4}}=1+\dfrac{4}{7}=\dfrac{11}{7}\)

Answer 4

 `1+1/(1+1/(1+1/3))`

\(=1+\dfrac{1}{1+\dfrac{1}{\dfrac{3}{3}+\dfrac{1}{3}}}\)

\(=1+\dfrac{1}{1+\dfrac{1}{\dfrac{4}{3}}}\)

\(=1+\dfrac{1}{1+1\times\dfrac{3}{4}}\)

\(=1+\dfrac{1}{1+\dfrac{3}{4}}\)

\(=1+\dfrac{1}{\dfrac{4}{4}+\dfrac{3}{4}}\)

\(=1+\dfrac{1}{\dfrac{7}{4}}\)

\(=1+1\times\dfrac{4}{7}\)

\(=1+\dfrac{4}{7}\)

\(=\dfrac{7}{7}+\dfrac{4}{7}\)

\(=\dfrac{11}{7}\)