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\begin{document}


\title{On-line Math 21}


\email{david.johnson@lehigh.edu}


\urladdr{http://www.lehigh.edu/\textasciitilde{}dlj0}

\maketitle
\begin{example}
\( b_{n}=2^{n} \) 
\end{example}
\begin{description}
\item [Solution]This sequence is just the denominators of the previous example. As
\( n \) increases, \( b_{n}=2^{n} \) increases very quickly, and increases
without bound. So, we say that this sequence \emph{diverges}, or has no limit
as \( n \) goes to infinity. It is a bit more precise to say that the sequence
\emph{goes to infinity} in the limit, or \[
\lim _{n\rightarrow \infty }2^{n}=\infty ,\]
since what happens is that the terms continue to grow (as opposed to varying
randomly). 
\item [Back]~\end{description}

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