\documentclass[12pt]{article}

\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{multicol}

\textwidth = 6.5 in
\textheight = 9 in
\oddsidemargin = 0.0 in
\evensidemargin = 0.0 in
\topmargin = 0.0 in
\headheight = 0.0 in
\headsep = 0.0 in
\parskip = 0.2in
\parindent = 0.0in

\title{Math 1b. Series---The Integral and Comparison Tests; Estimating Sums 
(Comparison Tests)}

\date{Spring 2006}

\begin{document}

\maketitle


\begin{enumerate}

\item 
Determine the convergence of the series
$$
\sum_{n=1}^\infty \frac{n^2 - 1}{3n^4 + 1}.
$$

\vfill

\item 
Determine the convergence of the series
$$
\sum_{n=1}^\infty \frac{n^2 - 1}{3n^4 + 1}.
$$

\vfill



\item 
Determine the convergence of the series
$$
\sum_{n=1}^\infty \frac{4 + 3^n}{2^n}.
$$

\vfill

\clearpage

\item 
Determine the convergence of the series
$$
\sum_{n=1}^\infty \frac{1 + \sin n}{10^n}.
$$

\vfill

\item 
Estimate the series
$$
\sum_{n=1}^\infty \frac{1}{n^{3/2}}
$$
to within 0.01.

\vfill

\item
If we estimate $\sum_{n=1}^\infty 1/n^{3/2}$ by
$$
\sum_{n=1}^{10} \frac{1}{n^{3/2}},
$$
how accurate is our estimate?


\vfill



\end{enumerate}





 \end{document}