de la cruz (cld2889) - HW010 - berg - (54070) This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page - find all choices before answering. 001 10.0 points 004 is conditionally convergent, absolutely convergent or divergent. 10.0 points XTo apply the root test to an infinite series an the value of n Determine whether the series 4 4 4 4 4 + + ... 3 4 5 6 7 1 = lim |an |1/n n has to be determined. Compute the value of for the series \u0012 \u0013n X 6n + 5 5 . n 4 1. series is absolutely convergent n=1 2. series is divergent 3. series is conditionally convergent 002 10.0 points 1. = 5 4 2. = 25 4 Determine whether the series X (1) n1 n=1 e1/n 6n is absolutely convergent, conditionally convergent or divergent. 3. = 4 4. = 15 2 5. = 4 5 1. absolutely convergent 2. conditionally convergent 3. divergent 005 10.0 points XTo apply the root test to an infinite series ak , the value of k 003 10.0 points = lim |ak |1/k k Determine whether the series X n=0 1 cos(n) n+5 has to be determined. Compute the value of for the series X 5 (ln k + 6)k . k k is conditionally convergent, absolutely convergent or divergent. 1. divergent k=1 1. = 30 2. conditionally convergent 2. = 5 3. absolutely convergent 3. = 0 de la cruz (cld2889) - HW010 - berg - (54070) 2 Determine whether the series 4. = 6 X (3)n (2n)! 5. = n=0 006 10.0 points XTo apply the ratio test to the infinite series an , the value n an+1 = lim n an has to be determined. Compute for the series X n=1 4n . 5n4 + 8 is absolutely convergent, conditionally convergent, or divergent. 1. conditionally convergent 2. absolutely convergent 3. divergent 009 Determine whether the series X (1)n+7 3 n 4 1. = 13 2. = n=1 1 2 is absolutely convergent, conditionally convergent, or divergent. 3. = 0 4. = 10.0 points 1. divergent 4 5 2. conditionally convergent 5. = 4 3. absolutely convergent 007 10.0 points Determine whether the following series X n=1 (1)n1 4n 5n2 + 2 010 10.0 points Determine whether the series X (1)n+1 n=3 is absolutely convergent, conditionally convergent, or divergent. ln n 5n 2 converges conditionally, converges absolutely, or diverges. 1. divergent 1. diverges 2. conditionally convergent 3. absolutely convergent 008 10.0 points 2. converges absolutely 3. converges conditionally de la cruz (cld2889) - HW010 - berg - (54070) Determine which, if any, of the series 011 10.0 points A. 1 + Which, if any, of the following statements are true? X A. If lim an = 0, then an converges. n X X B. If an is divergent, then |an | is divergent. C. TheX Ratio Test can be used to determine whether 1/n! converges. B. 1 1 1 1 + + + +... 2 4 8 16 X m+2 (m ln m)2 m=3 are convergent. 1. neither of them 2. B only 1. A and C only 3. A only 2. A and B only 4. both of them 014 3. none of them 10.0 points Determine which, if any, of the series 4. C only A. 5. B only X k+2 k 3k k=1 6. B and C only B. X n=2 7. A only 3 n n n2 are convergent. 1. neither of them 8. all of them 012 10.0 points Which one of the following properties does the series X k (1)k 2 k +3 k=2 2. B only 3. A only 4. both of them have? 015 10.0 points 1. conditionally convergent Determine which, if either, of the series 2. absolutely convergent A. 3. divergent 013 10.0 points B. X n=1 X k=3 (1)n1 2n 3 n4 + 5 (1)k 2 ln(k + 3) 3 de la cruz (cld2889) - HW010 - berg - (54070) are conditionally convergent. B. 4 X 5n n2 n! n=1 1. neither of them are convergent. 2. B only 1. B only 3. both of them 2. both of them 4. A only 016 10.0 points 3. neither of them Determine whether the series X (1) n1 n=1 \u0010 1\u0011 cos 4n is absolutely convergent, conditionally convergent or divergent. 4. A only 019 10.0 points Determine whether the series X 1. series is divergent 2en n! n=1 2. absolutely convergent 3. conditionally convergent is absolutely convergent, conditionally convergent, or divergent. 1. divergent 017 10.0 points Determine whether the series X (1)n1 n=1 e1/n 7n is absolutely convergent, conditionally convergent or divergent. 1. divergent 3. conditionally convergent 020 10.0 points Determine whether the series X m m1 (1) 4m + 7 m=1 2. conditionally convergent 3. absolutely convergent 018 2. absolutely convergent 10.0 points is absolutely convergent, conditionally convergent or divergent. 1. divergent 2. conditionally convergent 3. absolutely convergent Determine which, if any, of the series A. X n=1 1 ( 5 1)n n