hw1 - $\{a_n\}$ are of the form $\frac{1 \pm...

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\documentclass{amsart} \begin{document} \title{Math 145: Homework 1} \author{Andrew Berget} \maketitle Do not hand in the [bracketed] problems, they are simply suggestions of what might be a good problem for you to practice with. Once you feel comfortable with these you should be able to do the unbracketed problems. These problems are due Monday January 11. \bigskip Do Problems [2.5], [2.9], [2.10], 2.17 and [2.28] from the text. \bigskip Do Problem 2.22 from the text. In addition, prove (by induction?) that the sequence $\{a_n\}$ is either increasing or decreasing (you decide which). Next prove that the only possible limits of the sequence
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Unformatted text preview: $\{a_n\}$ are of the form $\frac{1 \pm \sqrt{29}}{2}$. Use the fact below, to prove that the limit $\lim_{n \to \infty} a_n$ exists and compute its value. \textbf{Fact.} A bounded monotonic sequence converges. \bigskip Do Problems [3.1], [3.2], [3.11], 3.25, 3.26, 3.32, 3.33+, 3.36, 3.41+. \bigskip \textbf{Problem A.} If two numbers between $1$ and $100$ are picked at random, what is the probability that the numbers differ by $15$? \bigskip \textbf{Problem B.} If a fair coin is tossed $3n$ times determine the probability the number of heads is twice the number of tails? \end{document}...
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This note was uploaded on 11/13/2011 for the course MATH 145 taught by Professor Peche during the Winter '07 term at UC Davis.

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