%% 
%%  Der Mathematiksatz mit LaTeX, 1. Auflage 2009
%% 
%%  Example 6-3-2 on page 95.
%% 
%%  Copyright (C) 2009 Herbert Voss
%% 
%%  It may be distributed and/or modified under the conditions
%%  of the LaTeX Project Public License, either version 1.3
%%  of this license or (at your option) any later version.
%% 
%%  See http://www.latex-project.org/lppl.txt for details.
%% 

\documentclass[]{ttctexa}
\pagestyle{empty}
\setcounter{page}{6}
\setlength\textwidth{355.65944pt}
\AtBeginDocument{\setlength\parindent{0pt}}
\StartShownPreambleCommands
\usepackage{amsmath}
\StopShownPreambleCommands
\begin{document}
\begin{gather*}
  A = \lim _{n\rightarrow \infty }\Delta x\left( a^{2}+\left( a^{2}+2a\Delta x+\left(
       \Delta x\right) ^{2}\right)\right.\\
  +\left( a^{2}+2\cdot 2a\Delta x+2^{2}\left( \Delta x\right) ^{2}\right)
       +\left( a^{2}+2\cdot 3a\Delta x+3^{2}\left( \Delta x\right) ^{2}\right)\\
  + \ldots\\
  \left.+\left( a^{2}+2\cdot (n-1)a\Delta x +(n-1)^{2}
        \left( \Delta x\right) ^{2}\right) \right)\\
  = \frac{1}{3}\left( b^{3}-a^{3}\right)
\end{gather*}
\end{document}