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\textbf{Math 166: Honors Calculus II}
\hfill\makebox[2.5in][r]{Name:\hrulefill}

\textbf{Quiz 10}\quad {\sl April 12, 2000}

\begin{enumerate}

\item Determine whether each of the following series converges or
diverges.

  \begin{enumerate}[a)]

  \item $\sum_{n=1}^\infty \frac{n!}{\sqrt{(2n)!}}$

  \answerspace

  \item $\sum_{n=0}^\infty \bigg(\frac{n+2}{3n+4}\bigg)^{n^2}$

  \answerspace

  \item $\sum_{n=1}^\infty \sin\Big(n\pi+\frac{\pi}{n}\Big)$

  \answerspace

  \end{enumerate}

\item Prove that $\sum_{n=1}^\infty \frac{1}{n^s}$ converges for $s>1$ and
diverges for $s\le1$.

\answerspace

\end{enumerate}

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