Please solve these questions. Some of them maybe already done, but please check my answers to see if they are correct. Show all work that leads to your answers. Thanks, in advance! Reference: AP Classroom AP Calculus BC

If the series S = (-1) 241 1 non is approximated by the partial sum Sk = mon . what is the least value of k for which the alternating series error bound guarantees that |S - Sk | 1 only C P >0 D P NV for some positive integer N. Il. lim an = 0 Ill. Jantil N for some positive integer N. A I only B I and II only C Il and Ill only D I, II, and IllThe alternating series test can be used to check for convergence for which of the following series? [(- 1) 141 7124 100 II. (-1)241 n4 3 100n-43 IM : IM: III. (-1) +1 if n is odd an Where an = if n is even A None B I only C I and Ill only D I, II, and IllWhich of the following statements must be true about the series an with positive terms if lim n-0 A The series converges if I = B The series converges if I = 1. C The series converges if I = 2. D The series converges if I = co.Which of the following series can be shown to converge by using the ratio test? Vn A n + 10 n=1 00 B 102 In(n) C n=1 n2 00 n+1 D n=1 n4Which of the following series converge? e n! II. 1002 IM & il (n!)2 III. (2n)! A) I only B Ill only c) I and Il only D) I and Ill onlyCO Consider the series Z(1)"\"ow where o. > for all 1:. and the sequence {on} decreases with limit 0. which ofthe following statements is true? I: 1 The series converges absolutely. The series converges conditionally. The series diverges. @ There is not enough information to determine whether the series converges or diverges. \fWhich of the following series is absolutely convergent? (- 1)* A * 1 k B K 2 k (In k) cos k C IM k- +1 (-1 )*k D k- + 1m If the partial sum with three terms is used to approximate the value of the convergent series 2 (1)'I ' 1 n 5, what is the alternating series error bound? :1 3 G) i i n 7 8 9 1|] 3,, 0.473 0,157 0.459 0.171 m n The alternating series 2 (71)\" luk converges to S and l] i a}: i 1 5 mg tor all k The table above shows values of the partial sum S = Z (71);" 1cikforfnurvalues of n If SE is used to approximate the value Set the series, what is the alternating series error bound? k 1 I: L Q) 0157 n 235 D 302 U 316