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  \large\bfseries Math 24 \\ Assignment 1 \\ Due Monday 7 January 2002
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\noindent{\bfseries Reading}: Read Appendix C (pp. 510--513) and
section 1.1 and 1.2 of the text.  Come to class with questions and
comments on Monday!

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\noindent
{\bfseries Written assignment}: work problems \#1, 10, 13, 18 and 22
of section~1.2 in the text.  In addition, work the following problems.

\begin{ques}
  In no more than a page, write a summary of why induction is a valid
  method of proof.  Assume your audience is someone with little or no
  mathematical sophistication.
\end{ques}
\begin{ques}
  Use mathematical induction to prove that
  \begin{equation*}
    {1^{2}} + {2^{2}} + {3^{2}} + \dots + n^{2}=
    \sum_{i=1}^{n} i^{2} = \frac {n(n+1)(2n+1)}6.
  \end{equation*}
\end{ques}
\begin{ques}
  Use mathematical induction to prove that if $x\ge0$ and
  $n\in\mathbf{N}=\{\,1,2,3,\dots\,\}$, then $(1+x)^{n}\ge 1+nx$.
\end{ques}
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