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# A11_2011 - University of Toronto at Scarborough Department...

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MAT A37H Summer 2011 Assignment # 11 You will NOT submit any of these questions but you should make sure that you are able to answer them. Your TA may present solutions for a nonempty subset of these exercises during TUTORIAL in the week of Aug. 1st and Aug. 8th). STUDY: Chapter 22 (BMCT) and Chapter 23 (pg 471 - 482 only, and excluding the Cauchy Criterion and all theorems dealing with ’absolute convergence’) HOMEWORK PROBLEMS: 1. Show the sequence deﬁned by a 1 = 2, a n +1 = 1 2 ( a n + 6) if n 1, is convergent. 2. Determine whether the series X n =1 ± 1 n - 1 n + 1 ² is convergent or divergent. If it is convergent, then ﬁnd its sum. 3. Let a n = 2 n 3 n +1 . (a) Determine whether { a n } is convergent. (b) Determine whether a n is convergent. 4. Determine whether the series is convergent or divergent. If it is convergent, then ﬁnd its sum. (a) 1 + 0

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A11_2011 - University of Toronto at Scarborough Department...

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