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Unformatted text preview: MAT 135 – 200708 Review Problems for Final Exam • The following problems were given at Finals of previous years. For each problem there is a year followed by a number. The year is the year at which the problem was given and the number is the number of the problem in the Final booklet of that year. For instance [‘04, B.6] refers to Problem B.6 of the Final of April 2004. You can get the answers of the problem by looking at the solutions of the corresponding termtest. These solutions are available online at: http://www.math.utoronto.ca/ponge/teaching/200708/MAT135/MAT135.html . • The sign ? indicates that the problem is chalenging. • During the review on Thursday, April 10th, we will go over problems on Chapter 11 only . Problems on Chapter 11 Problem 1 (‘03, B.16) . Consider the following two series: I. ∑ ∞ n =0 ( 1) n n ! e n . II. ∑ ∞ n =2 ( 1) n n 2 n 3 1 . Which of the following statements is correct? (A) I and II both converge absolutely. (B) I and II both converge conditionally. (C) I and II both diverge. (D) I diverges and II converges conditionally. (E) I diverges and II converges absolutely. Problem 2 (‘04, B.14) . Consider the following two series: I. ∑ ∞ n =1 ( 1) n 5 2 n n ! . II. ∑ ∞ n =1 ( 1) n 3 n 1 n 3 / 2 +1 . Which of the following statements is correct? (A) I converges conditionally and II converges absolutely. (B) I diverges and II converges conditionally. (C) I and II both converge absolutely. (D) I converges absolutely and II converges conditionally. (E) I diverges and II converges conditionally. Problem 3 (‘06, B.12) . Consider the following two series: I. ∑ ∞ n =0 ( 1) n n ! n +4 n . II. ∑ ∞ n =2 ( 1) n 1 n √ ln n . Which of the following statements is correct? (A) I converges conditionally and II converges absolutely. (B) I diverges and II converges conditionally. (C) I diverges and II converges absolutely. (D) I and II both converge conditionally. (E) I and II both diverge....
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 Spring '08
 LAM
 Math, Taylor Series, Mathematical analysis, 2W, 4 years, 2 k, 1 k

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