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\tutorial{tutorial5}{Problems for Tutorial 5}{October 21, 1996}

\section {Optimal Bookstacking}

Prove that the stacking arrangement shown in class is optimal for
producing the most overhang with a given number of books. That is,
given $n$ books, show that the most overhang that can be produced is
$H_n$, the $n$th harmonic number.\\

\section {Some Limits}

Compute the following limits.

\begin {itemize}
\item $\sum_{i=1}^n \frac {1}{i(i+1)}$.
\item $ \lim_{n \rightarrow \infty}  1/n + 1/(n+1) + \ldots + 1/2n$
\end{itemize}


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