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\textbf{Math 165: Honors Calculus I}

\textbf{Assignment 5}\quad \emph{Sept. 6, 1999}

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\begin{enumerate}
\item Compute the row of Pascal's Triangle for $n = 8$.

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\item Show that the row of Pascal's Triangle that begins ${}\quad1\quad
n \quad\cdots\quad$ adds up to $2^n$, i.e., show that $2^n =
\sum_{k=0}^n{n\choose k}$.

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\item Show that $0 = \sum_{k=0}^n (-1)^k{n\choose k}$.

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\item Show that ${n\choose k} = {n\over k}{n-1\choose k-1}$.

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\end{enumerate}

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