1. Determine the convergence or divergence of the sequence with the given nth term. Show your work. [5 pts each] a. a = 2n +3 5n b. a, = 4n- +1 2. Determine the convergence or divergence of the following series. State which test you are using and show supporting work. [8 pts each] a. 2n+1 120 3n + 2 3" b. C. 1+ + ... 2V2 3V/3 4V/4 5V/5 d. 2n +1 HEI (n + 1 ) C. 5 1=0 2 3n +1 f. IM : 2n-1 Determine whether the series converges absolutely or conditionally or diverges (State which test(s) you are using and show supporting work). [12 pts each] a. E(-1)" 2n +1 b. 00 (-1)" IM In - 4 te that they diverge. Show all52. (tan '(2) - tan ' (n + 1)) Convergence or Divergence Which series in Exercises 53-76 converge, and which diverge? Give reasons for your answers. If a series converges, find its sum. 53. 54. E(V2) " 55. (-1)+13 56. EC1) in 57. cos 2 58. 8 59. -2n 60. In 37 IM: IM: IM: IM: IM: I: IM: IMB 61. 62. IM: IM: IMe IM: IMO IM: IM 2" 63. 64. 89 T 90. 65. 1000 66. 2" + 3" 2n + 4" 91. 67. 40 68. 30 4 4"1. Determine the convergence or divergence of the sequence with the given nth term. Show your work. [5 pts each] a. a = 2n +3 5n b. a, = 4n- +1 2. Determine the convergence or divergence of the following series. State which test you are using and show supporting work. [8 pts each] a. 2n+1 120 3n + 2 3" b. C. 1+ + ... 2V2 3V/3 4V/4 5V/5 d. 2n +1 HEI (n + 1 ) C. 5 1=0 2 3n +1 f. IM : 2n-1 Determine whether the series converges absolutely or conditionally or diverges (State which test(s) you are using and show supporting work). [12 pts each] a. E(-1)" 2n +1 b. 00 (-1)" IM In - 4 te that they diverge. Show allIn Exercises 18, use the Direct Comparison Test to determine if each series converges or diverges. 9. -71 points LarCale11 9.5.JIT.004 Find the limit. lim X +8 Need Help? Road It Watch it Talk to a Tutor 10. O -/2 points LarCalc11 9.5.088. Find all values of x for which the series below converges absolutely and converges conditionally. (If the answer is an interval, enter answer is a finite set of values, enter your answers as a comma separated list of values.) n= 1 (a) converges absolutely (b) converges conditionally Need Help? Read it Talk to a Tutor