exam_3_f08

# exam_3_f08 - X n =1 2-1 n n √ n 5 ∞ X n =1 n 100 n 6...

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1. Suppose that we define a sequence by setting a n +1 = 4 - a n for n 1. a. If a 1 = 1, does the sequence { a n } converge or diverge? b. If a 1 = 2, does the sequence { a n } converge or diverge?
Problems 2 - 6: Determine if the series converges absolutely, converges conditionally, or diverges. 2. X n =2 ( - 1) n n ln n 3. X n =1 5 + 2 n (1 + n 2 ) 2

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Unformatted text preview: X n =1 2 + (-1) n n √ n 5. ∞ X n =1 n ! 100 n 6. ∞ X n =1 (-1) n arctan n n 2 7. Suppose that the series ∞ X n =0 c n ( x-2) n converges when x = 4 and diverges when x =-1. Determine if the following series converge or diverge. You do not need to justify your answers and no partial credit is possible. a. ∞ X n =0 c n (-1) n b. ∞ X n =0 4 n c n c. ∞ X n =0 2 n c n d. ∞ X n =0 nc n 8. If f ( x ) = ∞ X n =1 ( x + 1) n n 4 n , ﬁnd the intervals of convergence for f ( x ) and f ( x ). 9. Find power series centered at a = 0 equal to the following functions. Be sure to state where (i.e. for what values of x ) these series representations are valid. a. a ( x ) = 1 x + 10 b. b ( x ) = x x 2 + 10 c. c ( x ) = ln ( x 2 + 10) 10. Find the Taylor series for f ( x ) = x 4-3 x 2 + 1 at the point a = 1. Calculus II, Exam 3 Work Page...
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