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\title{General Mathematics and Computational Science I}
\author{Exercise 10}
\date{October 16, 2007}
\maketitle

\begin{enumerate}

\item Show that
\begin{equation*}
  \binom{n+1}{k+1}
  = \sum_{j=k}^n \binom{j}{k}
\end{equation*}
for every $0 \leq k \leq n$.

\item Use the method of generating functions to find a closed form
expression for the members of the generalized Fibonacci sequence
\begin{gather*}
  a_0 = A \,, \\
  a_1 = B \,, \\
  a_n = a_{n-1} + a_{n-2} \,.
\end{gather*}

\end{enumerate}
\end{document}

