de la cruz (cld2889) - HW010 - berg - (54070) This print-out should have 20 questions. Multiple-choice questions may continue on the next column or...

de la cruz (cld2889) – HW010 – berg – (54070) 1 This print-out should have 20 questions.

Multiple-choice questions may continue on the next column or page – nd all choices before answering. 001 10.0 points Determine whether the series 4 3 4 4+ 4 5 4 6+ 4 7 . . .

is conditionally convergent, absolutely con- vergent or divergent.

1. series is absolutely convergent 2. series is divergent 3. series is conditionally convergent 002 10.0 points Determine whether the series n = 1 ( 1) n 1 e1 /n 6 n is absolutely convergent, conditionally con- vergent or divergent.

1. absolutely convergent 2. conditionally convergent 3. divergent 003 10.0 points Determine whether the series n = 0 1 n + 5 cos( n ) is conditionally convergent, absolutely con- vergent or divergent. 1. divergent 2. conditionally convergent 3. absolutely convergent 004 10.0 points To apply the root test to an in nite series n a n the value of = lim n | a n|1 /n has to be determined. Compute the value of for the series n = 1 6 n + 5 n 5 4 n .

1. = 5 4 2. = 25 4 3. = 4 4. = 15 2 5. = 4 5 005 10.0 points To apply the root test to an in nite series k a k , the value of = lim k | a k|1 /k has to be determined. Compute the value of for the series k = 1 5 k k (ln k+ 6) k .

1. = 30 2. = 5 3. = 0 de la cruz (cld2889) – HW010 – berg – (54070) 2 4. = 6 5. = 006 10.0 points To apply the ratio test to the in nite series n a n, the value = lim n a n+1 a n has to be determined. Compute for the series n = 1 4 n 5 n 4 + 8 .

1. = 4 13 2. = 1 2 3. = 0 4. = 4 5 5. = 4 007 10.0 points Determine whether the following series n = 1 ( 1) n 1 4n 5 n 2 + 2 is absolutely convergent, conditionally con- vergent, or divergent.

1. divergent 2. conditionally convergent 3. absolutely convergent 008 10.0 points Determine whether the series n = 0 ( 3) n (2 n)!

is absolutely convergent, conditionally con- vergent, or divergent. 1. conditionally convergent 2. absolutely convergent 3. divergent 009 10.0 points Determine whether the series n = 1 ( 1) n +7 3 n is absolutely convergent, conditionally con- vergent, or divergent. 1. divergent 2. conditionally convergent 3. absolutely convergent 010 10.0 points Determine whether the series n = 3 ( 1) n +1 ln n 5n 2 converges conditionally, converges absolutely, or diverges. 1. diverges 2. converges absolutely 3. converges conditionally de la cruz (cld2889) – HW010 – berg – (54070) 3 011 10.0 points Which, if any, of the following statements are true?

A. If lim n a n = 0, then an converges.

B. If an is divergent, then |a n| is divergent.

C. The Ratio Test can be used to determine whether 1/n ! converges.

1. A and C only 2. A and B only 3. none of them 4. C only 5. B only 6. B and C only 7. A only 8. all of them 012 10.0 points Which one of the following properties does the series k = 2 ( 1) k k k2 + 3 have?

1. conditionally convergent 2. absolutely convergent 3. divergent 013 10.0 points Determine which, if any, of the series A. 1 + 1 2+ 1 4+ 1 8+ 1 16+ . . .

B. m = 3 m + 2 (m lnm)2 are convergent. 1. neither of them 2. B only 3. A only 4. both of them 014 10.0 points Determine which, if any, of the series A. k = 1 k + 2 k3k B. n = 2 3 n n n 2 are convergent.

1. neither of them 2. B only 3. A only 4. both of them 015 10.0 points Determine which, if either, of the series A. n = 1 ( 1) n 1 2n 3 n4 + 5 B. k = 3 ( 1) k 2 ln( k+ 3) de la cruz (cld2889) – HW010 – berg – (54070) 4 are conditionally convergent.

1. neither of them 2. B only 3. both of them 4. A only 016 10.0 points Determine whether the series n = 1 ( 1) n 1 cos 1 4n is absolutely convergent, conditionally con- vergent or divergent. 1. series is divergent 2. absolutely convergent 3. conditionally convergent 017 10.0 points Determine whether the series n = 1 ( 1) n 1 e1 /n 7 n is absolutely convergent, conditionally con- vergent or divergent.

1. divergent 2. conditionally convergent 3. absolutely convergent 018 10.0 points Determine which, if any, of the series A. n = 1 1 ( n 5 1)n B.

n = 1 5 n n 2 n !

are convergent.

1. B only 2. both of them 3. neither of them 4. A only 019 10.0 points Determine whether the series n = 1 2 e n n !

is absolutely convergent, conditionally con- vergent, or divergent. 1. divergent 2. absolutely convergent 3. conditionally convergent 020 10.0 points Determine whether the series m = 1 ( 1) m 1 m 4 m + 7 is absolutely convergent, conditionally con- vergent or divergent. 1. divergent 2. conditionally convergent 3. absolutely convergent