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Unformatted text preview: M408D Practice problems for Exam #2 Directions . Indicate the correct answer for each problem by filling in the appropriate space, as in (A) ( ) (C) (D) (E). 1) The series summationdisplay k =2 k k- 1 is: (A) convergent. (B) divergent. 2) If the alternating series test is used to analyze summationdisplay k =2 (- 1) k +1 ln( k + 4) 3 ln(2 k ) , then we find that lim k b k = (A) 0. (B) 4 3 . (C)- 1 12 . (D) 1 3 . (E) 1 2 . 3) If a k = f ( k ), where 1 f ( x ) 5 for all real x 1, then we can conclude that: (A) The sequence a k k is convergent. (B) The series summationdisplay k =1 a k k is convergent. (C) Both A and B. (D) Neither A nor B. 4) What are all values of p for which the series summationdisplay n =1 e pn n 2 is convergent? (A) p < 0. (B) 0 p < 1. (C)- 1 < p < 0. (D)- 1 < p 0. (E) p 0. 5) The series summationdisplay k =1 k 3 5 k is: (A) absolutely convergent. (B) conditionally convergent. (C) divergent....
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- Spring '07