Convergence of series wit 39. n=2 41. how that e conver- ne whether - 1 n...

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Convergence of series wit 39. n=2 41. how that e conver- ne whether - 1 n n3+1 43. 45. n=1 3n+5 n(n - 1)(n-2) 1 n + Inn 1 COS n n=1 n 40. n=2 n7 +2n+1 en + n 42.2n-n 44. n=1 Hint: Compare with n-2 n=1 In(n + 4) n5/2 46. (1-2-1/") Hint: Compare with the harmonic series. n=1 In Exercises 47-76, determine convergence or divergence using any method covered so far. 1 47. -9 n=4 49. n=1 n 4n +9 n - 1 n5 51. 15+1 cos n 48. n2 50. n=1 n - cos n n 1 52. + sinn n=1 8 53. (4/5)-" n=5 54. IM n=1 1 3n2 es Inn na, proved using rison Test, to 55. n=2 8 1 n3/2 ln n 57. 41/k k=1 59. n=2 61. n=3 (In n)4 1 n lnn - n 56. n=2 58. n=1 60. (Inn) 12 n9/8 4n 5n - 2n 2n 60. 3" - 1 n=1 - 1 62. n(Inn) - n=3 64. n) n - 4n3/2 n3 n or x 0. in Section 2.6, > 2 [because 63. 65. nn 1+(-1)" 66. n n=1 67. ove convergence n=1 sin- 1 2n+1 69. 4" n=1 n=1 2+(-1)" n3/2 68. n=1 sin(1/n) n 70. n=3 -15 evn Convergence of series wit 39. n=2 41. how that e conver- ne whether - 1 n n3+1 43. 45. n=1 3n+5 n(n - 1)(n-2) 1 n + Inn 1 COS n n=1 n 40. n=2 n7 +2n+1 en + n 42.2n-n 44. n=1 Hint: Compare with n-2 n=1 In(n + 4) n5/2 46. (1-2-1/") Hint: Compare with the harmonic series. n=1 In Exercises 47-76, determine convergence or divergence using any method covered so far. 1 47. -9 n=4 49. n=1 n 4n +9 n - 1 n5 51. 15+1 cos n 48. n2 50. n=1 n - cos n n 1 52. + sinn n=1 8 53. (4/5)-" n=5 54. IM n=1 1 3n2 es Inn na, proved using rison Test, to 55. n=2 8 1 n3/2 ln n 57. 41/k k=1 59. n=2 61. n=3 (In n)4 1 n lnn - n 56. n=2 58. n=1 60. (Inn) 12 n9/8 4n 5n - 2n 2n 60. 3" - 1 n=1 - 1 62. n(Inn) - n=3 64. n) n - 4n3/2 n3 n or x 0. in Section 2.6, > 2 [because 63. 65. nn 1+(-1)" 66. n n=1 67. ove convergence n=1 sin- 1 2n+1 69. 4" n=1 n=1 2+(-1)" n3/2 68. n=1 sin(1/n) n 70. n=3 -15 evn