Diverges limit comparison 4 27 1k 27 converges

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Unformatted text preview: 100 = 0 29. converges; ratio test 1/k 9. converges; root test 17. converges; comparison 25. converges; ratio test 33. converges; ratio test 23. diverges; limit comparison 4 27 1/k 27. converges; comparison 35. converges; root test 43. 10 81 31. converges; ratio test: ak +1 /ak → 37. converges; root test 39. converges; ratio test 47. p ≥ 2 41. (a) converges; ak +1 /ak → 0 (b) diverges; ak +1 /ak → 2 45. The series k! k! converges. Therefore lim k = 0 by Theorem 11.1.5. k →∞ k kk 49. Set bk = ak r k . If (ak )1/k → ρ and ρ < 1/r , then (bk )1/k = (ak r k )1/k = (ak )1/k r → ρ r < 1 and thus, by the root test, bk = ak r k converges. SECTION 11.4 / 1. diverges; ak → 0 3. diverges; ak → 0 / 1/k 5. (a) does not converge absolutely; integral test (b) converges conditionally; Theorem 11.4.3 7. diverges; limit comparison 11. diverges; ak → 0 / 9. (a) does not converge absolutely; limit comparison 1/k (b) converges conditi...
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This note was uploaded on 10/12/2010 for the course MATH 12345 taught by Professor Smith during the Spring '10 term at University of Houston - Downtown.

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