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\title{Math 1b. Power Series}

\date{Spring 2006}

\begin{document}

\maketitle

\begin{enumerate}

\item
Find the interval and radius of convergence of
$\displaystyle \sum_{n=1}^\infty (x - 2)^n$

\vfill

\item
Suppose that the power series $\sum_{n = 0}^\infty a_n x^n$ converges if $x = -3$ and diverges if $x = 7$.  Indicate which of the following statements must be true, cannot be true, or may be true.
\begin{enumerate}

\item
The power series converges if $x = -10$.

\item
The power series diverges if $x = 3$.

\item
The power series converges if $x = 6$.

\item
The power series diverges if $x = 2$.

\item
The power series diverges if $x = -7$.

\item
The power series converges if $x = -4$.

\end{enumerate}

\clearpage

\item
Find the interval and radius of convergence of
$\displaystyle \sum_{n=2}^\infty \frac{(x - 3)^{2n}}{n^4}$

\vfill

\item
Find the interval and radius of convergence of
$\displaystyle \sum_{n=2}^\infty \frac{(x + 5)^{n}}{n \ln n}$

\vfill

\item
Find the interval and radius of convergence of
$\displaystyle \sum_{n=1}^\infty \frac{(x + 1)^{n}}{n}$

\vfill

\item
Give an example of a power series that converges on the interval $[-11, -3)$.


\vfill



\end{enumerate}



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