math135ReviewFinal0708

math135ReviewFinal0708 - MAT 135 – 2007-08 Review...

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Unformatted text preview: MAT 135 – 2007-08 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 term-test. These solutions are available online at: http://www.math.utoronto.ca/ponge/teaching/2007-08/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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math135ReviewFinal0708 - MAT 135 – 2007-08 Review...

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