%%
%% An UIT Edition example
%%
%% Example 06-03-2 on page 89.
%%
%% Copyright (C) 2010 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.
%%
%%
%% ====
% Show page(s) 1
%%
\documentclass[]{exaarticle}
\pagestyle{empty}
\setlength\textwidth{375.57637pt}
\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\times 2a\Delta x+2^{2}\left( \Delta x\right) ^{2}\right)
+\left( a^{2}+2\times 3a\Delta x+3^{2}\left( \Delta x\right) ^{2}\right)\\
+ \ldots\\
\left.+\left( a^{2}+2\times (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}
