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{
\bf Attendance Quiz \# 2 for Dr. Z.'s Number Theory
}
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{\bf NAME:} (print!) $\underline
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{\bf E-MAIL ADDRESS:} (print!) 
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{\bf 1.} 
(i) Guess  a nice formula by inspection (ii) Give a rigorous proof of your
guessed formula, using the Fundamental Theorem of Discrete Calculus 
(iii) Give a fully rigorous
Zeilberger-style proof.

$$
\sum_{i=1}^{n} (i-1)i \quad ,
$$

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{\bf 2.} Prove the following identity
(i) using the Fundamental Theorem of Discrete Calculus 
(ii) using a Zeilberger-style proof via checking special cases.

$$
\sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6} \quad .
$$



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