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# hw1 - a n are of the form 1 ± √ 29 2 Use the fact below...

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MATH 145: HOMEWORK 1 ANDREW BERGET 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. Do Problems [2.5], [2.9], [2.10], 2.17 and [2.28] from the text. 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 1 ± √ 29 2 . Use the fact below, to prove that the limit lim n →∞ a n exists and compute its value. Fact. A bounded monotonic sequence converges. Do Problems [3.1], [3.2], [3.11], 3.25, 3.26, 3.32, 3.33+, 3.36, 3.41+. Problem A. If two numbers between 1 and 100 are picked at random, what is the probability that the numbers diﬀer by 15? Problem B. If a fair coin is tossed 3 n times determine the probability the number of heads is twice the number of tails? 1...
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