chapter11probs

# chapter11probs - n ± x-1 2 ² n 39. ∞ X n =1 ( x-3) n...

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In questions 1 to 28, determine whether the series converges or diverges. 1. X n =1 ± 3 - n + 1 n 3 / 2 ² 2. X n =1 tan ± 1 n ² 3. X n =1 3 - cos n n 3 / 2 - 2 1

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4. X n =1 1 3 ² 2 n + 1 n i 5. X n =1 1 q ln( n + 1) 6. X n =2 1 n (ln n ) 2
7. X n =2 1 n ln n 8. X n =2 1 n (ln n ) 2 9. X n =2 1 (ln n ) 2 3

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10. X n =2 1 n (ln n )(ln ln n ) 11. X n =1 1 n ln(1 + n 3 ) 12. X n =2 1 n ln( n 4 ) 4
13. X n =10 n 2 2 n 3 - 1999 14. X n =1 n n 3 + 5 15. X n =5 n + 1 n 3 / 2 - 2 n 5

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16. X n =1 tan( 1 n ) n 17. X n =1 n sin ± 1 n ² 18. X n =1 3 n 2 n + 4 n 6
19. X n =1 arcsin ± 1 n ² 20. X n =1 1 n + n cos n 21. X n =1 arctan ± n 2 - 1 n 2 + n ² 7

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22. X n =1 5 n - n 4 n + n 2 23. X n =1 3 s 3 n 2 + 1 n 4 - n 3 24. X n =2 1 n 4 / 5 ln n 8
25. X n =1 n ! n n 26. X n =1 ( n !) 2 (2 n )! 9

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27. X n =1 ln n n 2 28. X n =1 e 1 /n n 2 10
In questions 29 to 36, determine whether the series converges absolutely, converges conditionally, or diverges. 29. X n =1 ( - 1) n n ! 3 n 30. X n =1 ( - 1) n 2 n 1 / 3 31. X n =1 ( - 1) n 5 n n ! 11

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32. X n =1 ( - 1) n n n - 4 33. X n =1 ( - 1) n 1 ln( n 2 ) 34. X n =1 ( - 1) n arcsin ± - 1 n ² 12
35. X n =1 ( - 1) n n - 1 2 n 2 + n + 1 36. X n =1 ( - 1) n 3 n - 2 n 13

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In questions 37 to 42, ﬁnd the interval of convergence of the power series. 37. X n =1 (3 x - 2) n n 3 n 38. X n =1 1

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Unformatted text preview: n ± x-1 2 ² n 39. ∞ X n =1 ( x-3) n √ n + 1 14 40. ∞ X n =1 (-3) n x n 41. ∞ X n =1 (-2) n √ n ( x + 3) n 42. ∞ X n =1 (-1) n (2 x + 3) n n ln n 15 43. Find the coeﬃcient of x 4 in the Taylor series for f ( x ) = ln(cos x ). 44. Find the coeﬃcient of x 3 in the Taylor series for f ( x ) = e x sin x . 45. Find the coeﬃcient of x 3 in the Taylor series for f ( x ) = e 3 x cos 2 x . 16 46. Find the coeﬃcient of x 4 in the Taylor series for f ( x ) = e sin x . 47. Find the coeﬃcient of x 4 in the Taylor series for f ( x ) = cos 2 x . 17...
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## This note was uploaded on 12/07/2011 for the course MATH 242 taught by Professor Wang during the Spring '08 term at University of Delaware.

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chapter11probs - n ± x-1 2 ² n 39. ∞ X n =1 ( x-3) n...

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