% Activity -- Power Series -- 8.5
%
\documentclass[12pt]{article}
\usepackage{amsmath,amsfonts,amssymb}
\setlength{\topmargin}{-.5in}
\setlength{\oddsidemargin}{0in}
\setlength{\textwidth}{6.5in}
\setlength{\textheight}{9in}
\pagestyle{plain}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{document}
\thispagestyle{empty}

\begin{center}
{\large \begin{bf}
Project Based Math 112, Fall 2001\\
Activity \S 8.5 --- Intervals of Convergence of Power Series \\[.25in]
\end{bf}}
\end{center}

\begin{enumerate}
\item Consider the power series $\sum_{n=1}^{\infty} n^p x^n,$ where $p$
is a positive, real number.  

\begin{enumerate}
\item Find the radius of convergence.
\vfill
\item Find expressions for the two series at the endpoints of the interval
of convergence.
\vfill
\item Determine whether the series in part (b) converge.
\vfill
\item What is the interval of convergence?
\vfill
\end{enumerate}

\newpage

\item Consider the power series $\sum_{n=1}^{\infty} \displaystyle
\frac{x^n}{n^p},$ where $p$ is a positive, real number. 

\begin{enumerate}
\item Find the radius of convergence.
\vfill
\item Find expressions for the two series at the endpoints of the interval
of convergence.
\vfill
\item Determine whether the series in part (b) converge. (hint: the answer
depends on $p$).
\vfill\vfill
\item What is the interval of convergence?
\vfill
\end{enumerate}

\end{enumerate}

\end{document}
