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\title{Math 1b. Series---Geometric Series}

\date{Spring 2006}

\begin{document}

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\begin{enumerate}

\item 
Suppose that the country of Pottsylvania spends \${2} billion and that each recipient of a fraction of this wealth spends 90\% of the dollars that he or she receives.  In turn, the secondary recipients spend 90\% of the dollars that they receive, and so on.  What is the total spending that results from the original injection of \${2}~ billion dollars into the economy?

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\item
Determine the convergence of each of the following geometric series.  If the series converges, find its sum.
\begin{enumerate}

\item 
$1 + 0.4 + 0.16 + 0.064 + \cdots$

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\item
$\displaystyle \sum_{n = 0}^\infty \frac{(-6)^n}{5^n}$

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\item
$\displaystyle \sum_{n = 2}^\infty \frac{3^n}{\pi^n}$

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\end{enumerate}


\item
Express $6.254254\ldots$ as a ratio of two integers.

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\item
A ball is dropped from a height of 6 ft.  Each time the ball bounces, it comes back up to one-half of its previous height.  What is the total distance that the ball travels?


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\end{enumerate}

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