T4Solutions

T4Solutions - MATH 1005A Test 4 Solutions[Marks Questions 1...

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MATH 1005A Test 4 Solutions March 23, 2010 Questions 1 and 2 are multiple choice. Circle the correct answer. Only the answer will be [Marks] marked. 1. Which of the following series converge(s)? (i) 1 X n =0 3 2 n (ii) 1 X n =1 ( ¡ 1) n n (iii) 1 X n =1 1 n [3] (a) All (b) (i) and (ii) (c) (i) and (iii) (d) (ii) and (iii) (e) None Solution: (b) 2. Which of the following series converge(s)? (i) 1 X n =1 2 n n n (ii) 1 X n =1 n n n ! (iii) 1 X n =1 3 n ¢ 2 n [3] (a) All (b) (i) and (ii) (c) (i) and (iii) (d) (ii) and (iii) (e) None Solution: (c) 3. Determine whether the given series converges absolutely, converges conditionally, or diverges. Justify your answer. (a) 1 X n =1 ( ¡ 1) n n p n 2 +1 [4] Solution: The series diverges by the n th -term test since lim n !1 a n 6 =0(doesnotexist). (b) 1 X n =1 ( ¡ 1) n n 2 +1 [4] Solution: The series converges absolutely by the comparison test since ¯ ¯ ¯ ¯ ( ¡ 1) n n 2 +1 ¯ ¯ ¯ ¯ = 1 n 2 +1 1 n 2 and 1 X n =1 1 n 2 converges since it is a
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T4Solutions - MATH 1005A Test 4 Solutions[Marks Questions 1...

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