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1124worksheet10

# 1124worksheet10 - (c ∞ X n =1 4 n n 2 n 8(7 Determine...

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Polytechnic Institute of NYU MA 1124/1424 Worksheet 10 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 Total 100 1

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2 (1) Use the integral test to decide whether the series converge or diverge. (a) X n =1 1 2 n - 1 (b) X n =1 1 3 n (c) X n =1 ln n n (d) X n =1 1 e πn
3 (2) Use the comparison test to determine whether the series converges or diverges. (a) X n =1 2 n ( n + 2) (b) X n =1 n ( n + 3)( n + 2) (c) X n =1 n e n (d) X n =1 ln n n

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4 (3) Use the comparison test to determine whether the series converges or diverges. (a) X n =1 n + 1 n 3 n - 2 (b) X n =1 1 (3 n + 1) 2 (c) X n =1 n + 1 n 2 + 1 (d) X n =1 n ( n + 1) 2 - n
5 (4) Use the comparison test to determine whether the series converges or diverges. (a) X n =3 1 n 2 - 4 (b) X n =1 n 2 + 1 n 4 + 1 (c) X n =1 n + 1 n 2 n (d) X n =1 1 + 2 n 1 + 3 n

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6 (5) Determine whether the series converges or diverges. (a) X n =1 k ! 10 4 k (b) X n =1 k ! ( k + 2)! (c) X n =1 k !(2 k )! (3 k )!
7 (6) Determine whether the series converges or diverges. (a) X n =1 (2 n )! n 4 (b)

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Unformatted text preview: (c) ∞ X n =1 4 n ( n + 2) n 8 (7) Determine whether the series converges or diverges. (a) ∞ X n =1 ± n n + 100 ² n (b) ∞ X n =1 2 n n ! n n (c) ∞ X n =1 ± 1 n ² n 9 (8) Determine whether the series converges or diverges. (a) ∞ X n =1 (2 n + 1) 2 n (5 n 2 + 1) k (b) ∞ X n =1 n n (3 n ) 2 (c) ∞ X n =1 n n 4 ( n 2 ) 10 (9) Determine whether given alternating series is absolutely convergent, conditionally convergent, or divergent. (a) ∞ X n =1 (-1) n +1 1 ( n !) 2 (b) ∞ X n =1 (-1) n +1 n 2-3 n 2 + n + 2 (c) ∞ X n =1 (-1) n +1 n n 2 + 1 11 (10) Determine whether the series is absolutely convergent, conditionally convergent, or divergent. (a) ∞ X n =1 (-1) n 2 n n 2 + 1 (b) ∞ X n =1 (-1) n 2 n 3 n-4 (c) ∞ X n =1 cos πn n 2...
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