\documentclass [12pt]{article}
\oddsidemargin=0pt
\topmargin=0pt
\textwidth=6.5in
\textheight=8.5in
\begin{document}
\begin{center}
{\large\bf\LaTeX\ Example 8}
\end{center}
Sometimes we have to typeset a sequence of calculations:
\begin{align}
\sum_{r=1}^k\left( l(r)-l(r-1)\right)
&= \sum_{r=1}^k\left(N-2r+1\right) \\
&= k(N+1)-2\sum_{r=1}^kr \\
&= k(N+1)-k(k+1) \\
&= k(N-k)
\end{align}
\begin{quote}
\begin{verbatim}
\begin{align}
\sum_{r=1}^k\left( l(r)-l(r-1)\right)
&= \sum_{r=1}^k\left(N-2r+1\right) \\
&= k(N+1)-2\sum_{r=1}^kr \\
&= k(N+1)-k(k+1) \\
&= k(N-k)
\end{align}
\end{verbatim}
\end{quote}
Here is another way:
\begin{eqnarray*}
\sum_{r=1}^k\left(l(r)-l(r-1)\right)
&=& \sum_{r=1}^k\left(N-2r+1\right) \\
&=& k(N+1)-2\sum_{r=1}^kr \\
&=& k(N+1)-k(k+1) \\ &=& k(N-k)
\end{eqnarray*}
\begin{quote}
\begin{verbatim}
\begin{eqnarray*}
\sum_{r=1}^k\left(l(r)-l(r-1)\right)
&=& \sum_{r=1}^k\left(N-2r+1\right) \\
&=& k(N+1)-2\sum_{r=1}^kr \\
&=& k(N+1)-k(k+1) \\ &=& k(N-k)
\end{eqnarray*}
Observations:
\begin{itemize}
\item The eqnarray environment is a displayed array with three columns. It is aligned on
the center column.
\item The \verb+*+ supresses the generation of equation numbers.
\end {itemize}
---Britney Wiggins
\end{document}
答案1
\usepackage{amsmath}
需要使用数学环境align, aligned, gather, gathered, multline等。
答案2
首先，为了使用align环境，您需要在开始时加载amsmath（或mathtools）包。其次，您需要通过在适当的位置添加相应的命令来关闭verbatim和环境。第三，现在是过时的命令，请尝试使用。quote\bf\bfseries
修复代码如下：
\documentclass[12pt]{article}
\oddsidemargin=0pt
\topmargin=0pt
\textwidth=6.5in
\textheight=8.5in
\usepackage{mathtools}
\begin{document}
\begin{center}
{\large\bfseries\LaTeX\ Example 8}
\end{center}
Sometimes we have to typeset a sequence of calculations:
\begin{align}
\sum_{r=1}^k\left( l(r)-l(r-1)\right)
&= \sum_{r=1}^k\left(N-2r+1\right) \\
&= k(N+1)-2\sum_{r=1}^kr \\
&= k(N+1)-k(k+1) \\
&= k(N-k)
\end{align}
\begin{quote}
\begin{verbatim}
\begin{align}
\sum_{r=1}^k\left( l(r)-l(r-1)\right)
&= \sum_{r=1}^k\left(N-2r+1\right) \\
&= k(N+1)-2\sum_{r=1}^kr \\
&= k(N+1)-k(k+1) \\
&= k(N-k)
\end{align}
\end{verbatim}
\end{quote}
Here is another way:
\begin{eqnarray*}
\sum_{r=1}^k\left(l(r)-l(r-1)\right)
&=& \sum_{r=1}^k\left(N-2r+1\right) \\
&=& k(N+1)-2\sum_{r=1}^kr \\
&=& k(N+1)-k(k+1) \\ &=& k(N-k)
\end{eqnarray*}
\begin{quote}
\begin{verbatim}
\begin{eqnarray*}
\sum_{r=1}^k\left(l(r)-l(r-1)\right)
&=& \sum_{r=1}^k\left(N-2r+1\right) \\
&=& k(N+1)-2\sum_{r=1}^kr \\
&=& k(N+1)-k(k+1) \\ &=& k(N-k)
\end{eqnarray*}
\end{verbatim}
\end{quote}
Observations:
\begin{itemize}
\item The eqnarray environment is a displayed array with three columns. It is aligned on
the center column.
\item The \verb+*+ supresses the generation of equation numbers.
\end {itemize}
---Britney Wiggins
\end{document}