\documentclass[12pt]{article}
\usepackage{fullpage,amsmath,amsfonts,graphicx}

\begin{document}

\title{General Mathematics and Computational Science I}
\author{Exercise 13}
\date{November 14, 2006}
\maketitle

\begin{enumerate}

\item (From Ivanov, p.\ 28.)  Let
\[
  a_n = \frac{n!}{n^n} \,.
\]
Show that
\[
  \lim_{n\to\infty} \frac{a_n}{a_{n+1}} = e \,.
\]

\item Use Stirling's formula to prove that
\[
  \frac{n!}{(n/2)!^2} \sim 2^n \, \sqrt{\frac{2}{\pi n}} \,.
\]

\end{enumerate}
\end{document}
