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\begin{center}
{\Large Warm-Up Problems and Lecture Problems

March 31, 2003}
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\begin{enumerate}

\item  Find the pattern for the following sequences.  Write the formula for the $n$-th term of the sequence.  (Hint: the idea for all of them are similar.)
\begin{enumerate}
\item  $1,2,4,8, \ldots$

\item  $\frac{1}{2}, \frac{3}{4}, \frac{9}{8}, \frac{27}{16}, \ldots$

\item  $100, 20, 4, \ldots$

\item  $100, -20, 4, \ldots$
\end{enumerate}

\item  Can you find the sum of the sequences above (using your calculator, can you estimate the sum?)

\vspace{1in}
\item  Consider the series:
	\[
	\sum_{n=1}^{\infty} \frac{1}{n+4} - \frac{1}{n+5}
	\]
	Write down the series term by term and find the sum.


\end{enumerate}


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