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\title{General Mathematics and Computational Science I}
\author{Exercise 17}
\date{November 15, 2007}
\maketitle

\begin{enumerate}


\item Show that
\[
  \sum_{i=1}^n i \, (-1)^{n-i} = \frac{2n+1-(-1)^n}4 \,.
\]

\item Solve the difference equation 
\[
  x_{n+1} = -x_n + (n+1) \,.
\]

\item A loan of $L$ Euros is to be amortized by equal monthly
payments.  The yearly interest rate is $r$, compounded monthly.
Derive a formula for the monthly payment required to pay off the loan
in $T$ years.


\end{enumerate}
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