Fall 2002 Infinite Series Problems From Old Exams

Thomas' Calculus: Early Transcendentals

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Mat104 Fall 2002, Infinite Series Problems From Old Exams 1. n =0 n 2 2 n 3 + 1 2. n =0 2 n n ! 3. n =0 n 2 2 n 4. n =0 n 4 + 7 n 3 + 3 3 n 5 + 8 n 2 + 2 5. n =0 n 2 + 2 n n 3 + 3 n 6. n =3 ( - 1) n ln(ln n ) 7. n =1 cos n 8. n =1 sin 1 n n 9. n =0 n 2 + 2 n + 4 n 5 + 4 n 4 + 2 10. n =1 2 n n 11. n =0 n 4 + n 3 n 5 + n 3 + n + 1 12. n =0 3 n · n ! (2 n )! 13. n =1 ( - 1) n sin 1 n 14. n =1 n ! n n 15. n =0 e ( - n 3 + n 2 + n ) 16. n =0 2 n + 6 n 7 n + 1 17. n =1 ( - 1) n 1 + 1 n n 18. n =1 cos 1 n n 19. n =1 sin 1 n n 20. n =1 2 n + 5 n n ! 21. n =2 ( - 1) n 1 ln 2 n + 2 22. n =0 n 4 · 2 - n 23. n =1 ln n n 24. n =0 6 n 4 + 7 n 3 + 1 n 6 + 3 n 2 + 5 25. n =4 1 n (ln n )(ln(ln n )) 2 26. n =1 5 n + 100 2 n 2 n + 9 n 27. n =1 ( - 1) n - 1 n 28. n =0 2 + - 1 3 n 2 n 29. n =0 n 2 e n 30. n =0 n 2 4 n 31. n =1 1 + 1 n n n 2 32. n =0 2 n - 3 n 4 n 33. n =1 n + 1 n + 2 · 1 n 1

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2 34. n =0 (1 . 01) n 35. n =0 sin 2 n n 2 + 1 36. n =0 7 n + 3 n 6 n + 4 n 37. n =1 5 n - 2 n 7 n + 3 n 38. n =1 3 n 2 + 5 n + 7 n 3 + ln n 39. n =1 ( n !) 2 (2 n )! 40. n =2 1 n ln( n 2 + 1) 41. n =0 n ! · 10 n (2 n )! 42. n =2 sin n n 2 ln n 43. n
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