documentclass{article}
usepackage{stackengine,amsmath}
stackMath
begin{document}
[
a_0 + frac{1}{displaystyle
  a_1 + frac{1}{displaystyle
    a_2 +stackunder{}{ddotsstackunder{}{displaystyle
      + frac{1}{displaystyle
        a_{n-1} + frac{1}{a_n}}}
}}}
]
end{document}