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

\textbf{Quiz 9}\quad {\sl April 6, 2000}

\begin{enumerate}

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\item Calculate the value of each of the following series.

  \begin{enumerate}[a)]

  \item $\sum_{n=0}^\infty \frac{2+(-1)^n}{5^{n+1}}$

  \answerspace

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

  [Hint: first find the partial fraction decomposition of
  $\frac{n+2}{n(n+1)}$ then use telescoping sums.]

  \answerspace

  \end{enumerate}

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

  \begin{enumerate}[a)]

  \item $\sum_{n=2}^\infty \frac{1}{\sqrt{n^2-1}}$

  \answerspace

  \item $\sum_{n=0}^\infty \frac{\sin(n^2)+1}{n^2+1}$

  \answerspace

  \end{enumerate}

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  \item Use the Comparison Test to prove the Limit Comparison Test.

  \answerspace

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