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{\bf Math 166: Honors Calculus II}
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{\bf Quiz 9}\quad {\sl Apr. 4, 1996}

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\item 
  \begin{enumerate}[a)]
  \item Prove that $\sum_{n=0}^\infty x^n$ converges to $\frac{1}{1-x}$
  if $|x|<1$.

  \answerspace

  \problemspace
  \item Prove that $\sum_{n=1}^\infty \frac{1}{n}$ diverges.

  \answerspace

  \end{enumerate}


\newpage
\item Prove that the series converges to the indicated sum.
  \begin{enumerate}[a)]

  \item $\sum_{n=0}^\infty \frac{3^{n-1}+4^{n+1}}{5^n} = \frac{125}{6}$.

  \answerspace

 
\item $\sum_{n=1}^\infty \frac{n}{(n+1)!} = 1$. (Hint: Show that
$\frac{n}{(n+1)!} = \frac{1}{n!} - \frac{1}{(n+1)!}$).

  \answerspace

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