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\title{Math 1b. Series---Other Convergence Tests 
(The Ratio Test)}

\date{Spring 2006}

\begin{document}

\maketitle

\begin{enumerate}

\item
Determine the convergence of $\displaystyle \sum_{n=1}^\infty \frac{n!}{(2n)!}$.

\vfill

\item
Determine the convergence of $\displaystyle\sum_{n=1}^\infty \frac{n!}{(n+2)!}$.

\vfill

\item
Determine the convergence of $\displaystyle\sum_{n=1}^\infty \frac{1}{\sqrt[3]{n^2 - 1}}$.

\vfill

\clearpage

\item
Determine the convergence of $\displaystyle\sum_{n=1}^\infty \frac{\arctan n}{1 + n^2}$.

\vfill

\item
Determine the convergence of $\displaystyle\sum_{n=1}^\infty \frac{n^3}{n^5 + 4}$.

\vfill

\item
Determine the convergence of $\displaystyle\sum_{n=1}^\infty \frac{1}{n 3^n}$.

\vfill

\item
Determine the convergence of $\displaystyle1 + \frac{1}{1 \cdot 3} + \frac{1}{1 \cdot 3 \cdot 5} + \frac{1}{1 \cdot 3 \cdot 5 \cdot 7} + \cdots $.

\vfill


\end{enumerate}


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