\documentclass[11pt]{article}
\usepackage{handout2e}
\begin{document}
\input{macros}
\input{courseMacros}
\thispagestyle{empty}
\setlength{\parindent}{0pt}
\setlength{\parskip}{1.8ex}

\head{CSU690}{Algorithms and Data}{Spring 2005}{10 January 2005}{3}

\begin{center}
\Large{\bf Recitation 1}
\end{center}

{\bf 1.} Prove by induction on $n \ge 0$ that 

\[
\sum_{i = 1}^n i^3 = \frac{n^2(n+1)^2}{4}.
\]

{\bf 2.} Exercise 2.2-2, page 27.

{\bf 3.} Arrange the following functions in order from the slowest
growing function to the fastest growing function.  Briefly justify
your answers.  ({\em Hint:} It may help to plot the functions and
obtain an estimate of their relative growth rates.  It may also help
to express each function as a power of $2$ and then compare.)

\[
(\lg n)^{20} \hs \hs n^{1/4} \hs \hs 2^{n/100}
\]

\end{document}