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{\bf Math 166: Honors Calculus II}
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{\bf Quiz 9}\quad {\sl Apr. 6, 1995}

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\item 
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  \item Prove that $\sum_{n=0}^\infty x^n$ converges to $\frac{1}{1-x}$ if $|x|<1$.

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

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

  \item $\sum_{n=1}^\infty \frac{2^{n-1}+3^{n+1}}{4^n} = \frac{19}{2}$.

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\item $\sum_{n=2}^\infty \log(1-\frac{1}{n^2}) = -\log(2)$. (Hint: Use
telescoping series).

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