homework_example.tex

\documentclass{homework}

\class{CS 1234: Repeatedly Greeting the Universe}
\homework{2}{: How to Count}

\begin{document}
\maketitle

\begin{enumerate}
  \item 
  \begin{enumerate}
    \item
    \begin{itemize}
      \item I can count!
      \item Of course I can count.
      \item Counting is cool.
    \end{itemize}
    \item \TODO
  \end{enumerate}
  \item 
  \begin{proof}
      Let $P(n)$ be the statement that $\sum_{i=1}^{n}i = \frac{n(n + 1)}{2}$.\\
      \bc $P(1)$ is true, since $\frac{1*(1+1)}{2}= 1$.\\
      \is Assume that $P(k)$ is true where $k$ is an arbitrary fixed integer greater than 1. We will prove that $P(k)$ is true; in other words, that $\sum_{i=1}^{n+1}i = \frac{(n+1)(n + 2)}{2}$
      \begin{align*}
      \sum_{i=1}^{n+1}i &=\sum_{i=1}^{n}i + n + 1 \numberthis \label{cooleqn}\\
      &= \frac{n(n + 1)}{2} + (n+1)\ih\\
      &= \frac{n(n + 1) + 2(n+1)}{2}\numberthis\\
      &= \frac{(n+1)(n + 2)}{2} 
      \end{align*}
      This completes the inductive steps. Thus, by mathematical induction, $P(n)$ is true for all integers $n$ with $n \ge 1$.
  \end{proof}
  \item Wow, \eqref{cooleqn} is a cool equation.
\end{enumerate}
\end{document}