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\begin{itemize}
\item $\Sigma_{k=0}^r (n+k {\mbox choose } k) = (n+r+1 {\mbox choose } r)$.
\item Combinatorial and algebraic arguments for $\Sigma k (n {\mbox
    choose } k) = n2^{n-1}$.
\item Use of differentiation and integration in generating functions.
\item A bunch of generating function problems.
\end{itemize}


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