Continued fraction

Question

I am currently working on my bachelor thesis. I want to visualize a general continued fraction. I concatenate the fractions with the command \cfrac. The result is okay, but I rather want the last link (the one right next to the dots) to be a bit more below. Hopefully the picture makes clear what I mean. Do you have any ideas?

Here is a small example of my code:

\documentclass[11pt, a4paper, german]{scrartcl}
\usepackage[ngerman]{babel}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{mathabx}
\begin{document}
\begin{equation*}
    a_{0}+\cfrac{1}{a_1+\cfrac{1}{a_2+\cfrac{1}{a_3+\hspace{0.5cm}\ddots\hspace{0.5cm}\cfrac{1}{a_{n-1}+\cfrac{1}{a_n}} }}}
\end{equation*}
\end{document}

Answer 1

I just applied a \raisebox{<len>}{$...$} to the last term.

\documentclass[11pt, a4paper, german]{scrartcl}
\usepackage[ngerman]{babel}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{mathabx}
\begin{document}
\begin{equation*}
    a_{0}+\cfrac{1}{a_1+\cfrac{1}{a_2+\cfrac{1}{a_3+\hspace{0.5cm}\ddots
    \hspace{0.5cm}\raisebox{-3ex}{$\cfrac{1}{a_{n-1}+\cfrac{1}{a_n}}$} }}}
\end{equation*}
\end{document}

Answer 2

I'd lower also the \ddots:

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{equation*}
a_{0}+\cfrac{1}{
  a_1+\cfrac{1}{
    a_2+\cfrac{1}{
      a_3+\begin{array}[t]{c@{\;}c@{}}
          \\[-1.5ex]
          \ddots\\[-1.5ex]
          &{}+\cfrac{1}{a_{n-1}+\cfrac{1}{a_n}}
          \end{array}
      }
    }
  }
\end{equation*}

\end{document}