Please help me on these AP Calculus BC question on Sequences and Series! I would appreciate if you would should your work that leads to your answers. All of these questions are multiple choice questions, and some of them might already be completed. But try to check my answers to see if they are correct, too. Please feel free to tell the choice letter for each question and tell me the right answer for any one of the already answered questions, if I got it wrong. Thank you for all you do!

DO What are all values of & for which the series E ((k3 + 2)e *)" converges? A k = -1.314, k = -1.193, and k = 4.596 only B k 4.596 D k > 4.596 onlyIf S, is the nth partial sum of the infinite series an and n. > 3, which of the following is true? n=1 A On = Sn-1 - Sn 2 B an = Sn - Sn 1 C an = Sn41 - Sn D an = Snu - Sn-1If c is a positive real number and ax = In c for what values of c, if any, does the infinite series ax converge? K 1 A c = 1 only B c 1 only D There are no positive values of c for which the series converges.If by is a sequence of real numbers with n = 0, 1, 2, ... and an = bn - bn_1 for n = 1, 2, ..., which of the following is true about the infinite series an A The series converges if lim an = 0. 1 4:00 B The series converges if lim b, is a finite real number. 71 +00 C The series diverges if lim by * 0. n-+00 D The series has lim bn as its sum if lim bn is a finite real number.Ix: (xi If a. is nonzero real number and r is a real number with [l 1:: |r| 1:_ 1, what is the value of E a?\" E urn ? 1'1:I} r121 II) If m and y are nonzero real numbers such that |.1:y| .1: 1, what is the sum of the innite series E 5-32 _ n21 If the infinite series M8 an diverges, Sn. = ap and lim by / 0, which of the following statements must be true? I. lim an * 0 71 }:00 Il. lim S does not exist. 11 7:00 00 III. > bn diverges. n 0 A I only B II only C Il and Ill only D I and Ill onlyIf an = V2 for n = 1, 2, 3, ..., which of the following statements about On must be true? n 1 A The series converges and lim an = 0. B The series diverges and lim an = 0. C The series converges and lim an * 0. D The series diverges and lim an * 0. 1 +00The nth term test can be used te determine divergence for each of the following series except 2 : n The integral test can be used to conclude that which of the following statements about the innite series q is true? \"5"" + 1 {I} 11:1 The series converges, and the terms of the series have limit 0. The series diverges, and the terms of the series have limit [1 The series converges, and the terms of the series do not have limit 0. The series diverges, and the terms of the series do not have limit D. The integral test can be used to determine convergence or divergence for each of the following infinite series except 2 A 78 B n 1 4 + 6n COS n C n=1 en Inn D 7 2 n{III The integral test can be used to conclude that which of the following statements about the innite series E 11:1 The series converges, and the terms of the series have limit 0. The series diverges, and the terms of the series have limit [1 The series converges, and the terms of the series do not have limit D. The series diverges, and the terms of the series do not have limit E]. Which of the following is a divergent series? I. The harmonic series II. A p-series with p = III. A p-series with p = A I only B II only C I and II only D I, II, and Ill