MATH 141E Series Practice 2

MATH 141E Series Practice 2 - SAMPLE PROBLEMS Determine...

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Unformatted text preview: SAMPLE PROBLEMS Determine whether each of the following series converges or diverges. 1. 4. 7. 10. 13. 16. 19. 22. 25. 28. 31. 34. 37. 40. 43. 46. 49. 52. 55. 58. 1 n 2. 5. 8. 11. 14. 17. 20. 23. 26. 2 n n 1 n sin2 n n2 cos n+5 n2 ln n n 1 n2 ln n 1 n(ln n)2 ln n n2 n+1 n2 +1 n2 2n (n2 ) 3. 6. 9. 12. 15. 18. 21. 24. 27. 2 n 1 n! sin n n2 cos n+5 n 1 n ln n 1 n ln n 1 n ln n 1 n2 +1 n-2 n2 -1 e-n e(-1/n) 22n+3 5n-4 22n+3 3n-4 1 n(ln n)2 ln n n3 1 n2 -1 2n n2 1- 2 n n 1+ 1- n! (2n)! 29. 32. 35. 38. 41. 1- 30. 33. 36. 1+ n! nn 2 n (n2 ) 2 n (n3 ) 1+ 2 n (n3 ) 102n+5 n! (2n)! (2n+1)! 32n+1 (n!)2 1 n(n+1) 1 nln nln(ln n) n (n!)n n(n2 ) 5n (n!)3 (3n)! 2n n! 5 1+en 1 n sin( n ) 1 n cos( n ) 1 tan( n ln n ) (2n+1)! 3n (n!)2 (ln n)n nn 1 39. 42. 45. 48. 51. 54. 57. 60. nln n 1-n n2n ln(ln n) 44. 47. 50. 53. 56. 59. n 1 sin( n ) 1 sin( n2 ) n ln( n+1 ) 1 cos( n ) 1 n2 sin( n2 ) ln n ln(2n+1) 1 (cos( n ) - 1) (ln n- ln(2n+ 1)) ln(1 + 1 n2 ) (e(1/n ) - 1) 2 The series in the following problems converge: 3,4,5,6,8,10,14,16,19,20,21,22,26,29,31,33,34,35,36,38,39,40,41,42,45,46,52,58,59,60 The series in the other problems diverge. 1 ...
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MATH 141E Series Practice 2 - SAMPLE PROBLEMS Determine...

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