1124worksheet9

# 1124worksheet9 - Polytechnic Institute of NYU MA 1124/1424...

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Unformatted text preview: Polytechnic Institute of NYU MA 1124/1424 Worksheet 9 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 10 2 15 3 10 4 10 5 10 6 10 7 10 8 10 9 15 Total 100 1 2 (1) Find a formula for the general term a n of the sequence, assuming that the pattern of the first few terms continues. (a) 1 2 , 1 4 , 1 6 , 1 8 ,... (b) 3 16 , 4 25 , 5 36 , 6 49 ,... (c) 2 , 4 , 2 9 , 8 , 2 25 , 12 , 2 49 ,... (d) { , 2 , , 2 , , 2 ,... } 3 (2) Determine whether the sequence converges or diverges. If it converges, find the limit. (a) a n = 1 5 n 3 (b) a n = 3 √ n + 4 √ n √ n + √ 5 n (c) a n = n 2- n (d) a n = cos( nπ/ 2) (e) a n = n 2 n + 1 4 (3) Determine the monotonicity of the indicated sequence. (a) a n = 1 4 n + 5 (b) a n = n- 2 n + 2 (c) a n = sin( nπ/ 2) (d) a n = n n 2 + n- 1 5 (4) Determine the boundedness and the monotonicity of the indicated sequence....
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1124worksheet9 - Polytechnic Institute of NYU MA 1124/1424...

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