Question

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

Answer 1

1+1/(1+(1/(1+1/3))) = 11/7

Answer 2

$1 + 1/(1+(1/(1+ \frac{1}{3} )))\\=1 + 1/(1+(1/(\frac{4}{3} )))\\=1 + 1/(1+ \frac{3}{4} )\\=1 + 1/( \frac{7}{4} )\\=1+ \frac{4}{7} \\=\boxed{ \frac{11}{7} }$