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\noindent Quiz 3

\noindent Math 336, Winter `00

\vspace*{.2in}
\noindent 1.  Let $\sum_{j=1}^\infty a_n$ be a series.  When does the 
series converge and what is its sum equal to?

\vspace*{2.5in}

\noindent 2.  Following are four series.  Two converge and two diverge.
Identify one of the convergent ones and one of the divergent ones, 
and provide a short justification  in each case
(for example, name a test or state a
theorem that will
support your claim; if you name the comparison test, indicate which
series you want to compare with).
\begin{itemize}
\medskip
\item $\sum_{j=1}^\infty \frac{j^2 - 3j + 1 }{j^3 - 4j + 5}$
\medskip
\item $\sum_{j=1}^\infty e^{-j}\cos(\pi j/2)$
\medskip
\item $\sum_{j=1}^\infty \frac{\log j}{j^3}$
\medskip
\item $\sum_{j=1}^\infty \sqrt{j^2 + j} - j$
\end{itemize}

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