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\begin{center}
{\Large Warm-Up Problems and Lecture Problems

April 11, 2003}
\end{center}

\begin{enumerate}

\item  Determine if the following series converge or diverge.
	If the series converges, determine if the series converges conditionally or 
	if the series converges absolutely.
	\begin{enumerate}
	\item  $\sum_{n=2}^\infty (-1)^n \ln n$
\inch

	\item  $\sum_{n=2}^\infty (-1)^n \frac{1}{\ln n}$
\inch

	\item  $\sum_{n=1}^\infty (-1)^{n+1} \frac{n+2}{n^3}$
\inch

	\item  $\sum_{n=1}^\infty (-1)^{n+1} \frac{n+2}{n^2}$

	\end{enumerate}


\newpage
{\Large\textbf{Lecture and homework problems}}

\item  Using the ratio test, 
	determine the radius of convergence and the interval of convergence for the following series:
	\begin{enumerate}
	\item  $\sum_{n=0}^\infty 3^nx^n$
\inch

	\item  $\sum_{n=0}^\infty \frac{x^n}{3^n}$
\inch

	\item  $\sum_{n=1}^\infty \frac{x^n}{n3^n}$
\inch

	\item  $\sum_{n=0}^\infty \frac{nx^n}{3^n}$

	\end{enumerate}


\end{enumerate}


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