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\centerline
{
\bf ``QUIZ'' for March 10, 2006, Dr. Z.'s Colloquium talk
}
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{\bf NAME:} (print!) $\underline
{\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$

\bigskip
{\bf E-MAIL ADDRESS:} (print!) 
$\underline
{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
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{\bf 1.} Conjecture and prove an explicit expression for
$$
a(n):=\sum_{i=1}^{n} i \quad
$$
using the methodology of {\bf experimental mathematics}
(no credit for other methods!) .

{\bf Hint:} $a(n)$ is characterized by $a(n)-a(n-1)=n$ and
$a(0)=0$.

\end

