SalasSV_11_02_ex - 11.2 THE INTEGRAL TEST COMPARISON TESTS...

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EXERCISES 11.2 Determine whether the series converges or diverges. 1. k k 3 + 1 . 2. 1 3 k + 2 . 3. 1 (2 k + 1) 2 . 4. ln k k . 5. 1 k + 1 . 6. 1 k 2 + 1 . 7. 1 2 k 2 k . 8. ± 5 2 ² k . 9. tan 1 k 1 + k 2 . 10. ln k k 3 . 11. 1 k 2 / 3 . 12. 1 k ( k + 1)( k + 2) . 13. ± 3 4 ² k . 14. 1 1 + 2ln k . 15. ln k k . 16. 2 k (ln k ) 2 . 17. 1 2 + 3 k . 18. 7 k + 2 2 k 5 + 7 . 19. 2 k + 5 5 k 3 + 3 k 2 . 20. k 4 1 3 k 2 + 5 . 21. 1 k ln k . 22. 1 2 k + 1 1 . 23. 1 + 2 k 1 + 5 k . 24. k 3 / 2 k 5 / 2 + 2 k 1 . 25. 2 k + 1 k 4 + 1 . 26. 2 k + 1 k 3 + 1 . 27. 2 k + 1 k 5 + 1 . 28. 1 ³ 2 k ( k + 1) . 29. ke k 2 . 30. k 2 2 k 3 . 31. 2 + sin k k 2 . 32. 2 + cos k k + 1 . 33. 1 1 + 2 + ···+ k . 34. k 1 + 2 2 + ···+ k 2 . ² c 35. Use a CAS to determine the convergence or divergence of the series. (a) k = 0 2 k ! (2 k ) ! . (b) k = 0 2 k (2 k ) ! . (c) k = 0 2 k ! (2 + k ) ! . ² c 36. Use a CAS to evaluate the improper integral that will determine the convergence or divergence of the series. (a) k = 1 k 1 + k 2 . (b)
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SalasSV_11_02_ex - 11.2 THE INTEGRAL TEST COMPARISON TESTS...

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