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de la cruz (cld2889) – HW09 – berg – (54070) 1 This print-out should have 16 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Determine the convergence or divergence of the series (A) X∞ n = 2 n 2(ln n) 2 , and (B) X∞ n = 1 tan−1 n 1 + n4 . 1. A converges, B diverges 2. A diverges, B converges 3. both series diverge 4. both series converge 002 10.0 points If ak , bk , and ck satisfy the inequalities 0 < bk ≤ ck ≤ ak , for all k, what can we say about the series (A) : X∞ k = 1 ak, (B) : X∞ k = 1 bk if we know that the series (C) : X∞ k = 1 ck is divergent but know nothing else about ak and bk? 1. (A) diverges, (B) diverges 2. (A) converges, (B) need not converge 3. (A) diverges, (B) converges 4. (A) diverges, (B) need not diverge 5. (A) need not diverge , (B) diverges 6. (A) converges, (B) diverges 003 10.0 points Which, if any, of the following series converge? (A) X∞ n = 4 3 √ n(n − 3) (B) X∞ n = 1 1 + sin(n) 4 n 1. A and B 2. A but not B 3. neither A nor B 4. B but not A 004 10.0 points Which of the following series (A) X∞ n = 1 5n 3n2 + 5 (B) X∞ n = 1 5 6 n (C) X∞ n = 18 3 4 n converge(s)? 1. A, B, and C 2. B and C only de la cruz (cld2889) – HW09 – berg – (54070) 2 3. C only 4. B only 5. A and B only 005 10.0 points Which of the following series diverge(s)? (A) X∞ k = 1 2k 3 ln(k) + 6 (B) X∞ k = 1 3 2 k (C) X∞ k = 1 2k 2 6k 3 − 2 1. A, B, and C 2. A and C 3. B and C 4. B only 5. A only 006 10.0 points Which of the following series (A) X∞ k = 1 2k 7 ln k + 7 (B) X∞ k = 1 7 2 k (C) X∞ k = 1 2k 2 7k 3 − 2 converge(s)? 1. B and C 2. A and C 3. none of them 4. A only 5. B only 007 10.0 points Which of the following series (A) X∞ n = 1 5 7n log n + 6n (B) X∞ n = 1 6n n (n + 3)n (C) X∞ n = 1 3n 7n + 5n diverge? 1. A only 2. C only 3. A and C 4. A and B 5. All of them 008 10.0 points Which of the following series (A) X∞ n = 3 2n + 3 (n ln n) 2 + 5 (B) X∞ n = 1 √ n − 7 √ n + 3 (C) X∞ n = 1 7n + 3 5n − 2 n diverge(s)? de la cruz (cld2889) – HW09 – berg – (54070) 3 1. B only 2. all of A, B, C 3. A and B 4. C only 5. B and C 009 10.0 points Find all values of p for which the infinite series X∞ n = 1 5n 7 4n4 + 5p converges? 1. p > 3 2. p < −2 3. p < −3 4. p > 2 5. p > 1 3 6. p < − 1 3 010 10.0 points Which one of the following series is convergent? 1. X∞ n = 1 (−1)2n 2 3 + √ n 2. X∞ n = 1 (−1)n−1 4 + √ n 2 + √ n 3. X∞ n = 1 (−1)n−1 4 + √ n 4. X∞ n = 1 3 2 + √ n 011 10.0 points Which one of the following series is convergent? 1. X∞ n = 1 (−1)2n 2 3 + √ n 2. X∞ n = 1 (−1)n−1 4 + √ n 3. X∞ n = 1 (−1)n−1 4 + √ n 2 + √ n 4. X∞ n = 1 3 2 + √ n 5. X∞ n = 1 (−1)3 2 3 + √ n 012 (part 1 of 3) 10.0 points Decide whether the series X∞ n = 1 (−1)n−1 7n − 6 converges or diverges. 1. diverges 2. converges 013 (part 2 of 3) 10.0 points Decide whether the series X∞ n = 1 (−1)n−1 √ 7n 1 + √ n converges or diverges. 1. converges 2. diverges de la cruz (cld2889) – HW09 – berg – (54070) 4 014 (part 3 of 3) 10.0 points Decide whether the series X∞ n = 1 (−1)n−1 cos 1 n converges or diverges. 1. diverges 2. converges 015 10.0 points Find the smallest number of terms of the series X∞ k = 1 (−1)k k 3 k we need to add in order to estimate the sum of the series with error less than 8/3 8 . 1. #terms = 9 2. #terms = 7 3. #terms = 5 4. #terms = 6 5. #terms = 8 016 10.0 points Determine all values of p for which the series X∞ n = 2 (−1)n−1 (ln(n))p 3n is convergent, expressing your answer in interval notation. 1. [0, ∞) 2. (−∞, ∞) 3. p = {0} 4. (0, ∞) 5. (−∞, 0)