The following series has the following terms: 2020 + sin(n) ay = 1, an+1 = —...
7 TT 5. For the following series, 1 1 sin + - sin + = sin + sin +. 4 2 9 3 16 4 (a) (5 points) Write the general term an (b) (15 points) Determine whether the series converges or diverges by using integral test. Hint: In the integral use u = substitution. n
True of False (g) does the power series from ∞ to n=1 (x−2)^n /n(−3)^n has a radius of convergence of 3. (h) If the terms an approach zero as n increases, then the series an converges? (i) If an diverges and bn diverges, then (an + bn) diverges. (j) A power series always converges at at least one point. (l) The series from ∞ to n=1 2^ (−1)^n converges?
1 sin )-sin Determine whether the following series converge or diverge. +1 Select one a. Diverges b. Converges, and the partial sum is 1 C. Converges, and the partial sum is sin 1 2 d. Converges, and the partial sum is 0
Determine whether the series converges or diverges. n + 1 Σ +n n = 1 The series converges by the Limit Comparison Test. Each term is less than that of a convergent geometric series. The series converges by the Limit Comparison Test. The limit of the ratio of its terms and a convergent p-series is greater than 0. The series diverges by the Limit Comparison Test. The limit of the ratio of its terms and a divergent p-series is greater...
Do the following series converges or diverges. Justify your answer. (a) sin?(n) n2 n= i M8 M8 nh (b) 22n 221 n=1
Determine whether the following series converges 7k+1 Let , represent the magnitude of the terms of the given series, Select the correct choice below and fill in the answer box(es) to complete your choice. OM. The series converges because is nonincreasing in magnitude for k greater than some index N and limax- 00 OB. The series diverges because is nondecreasing in magnitude for k greater than some index N. OC. The series diverges because is nonincreasing in magnitude for k...
2. (a) Determine if the following series converges or diverges. 2" No n+1 (b) Determine if the following geometric series converges or diverges. If it converges, find the sum. 0.444444...
n+00 1. A series an has the property that lim an = 0. Which of the following is true? n=1 (a) The series converges and has the sum 0. (b) The series is convergent but its sum is not necessarily 0. (c) The series is divergent. (d) There is not enough information to determine whether the series converges or diverges.
(6 pts) Match each of the following with the correct statement. A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent. D. The series diverges Vn (n + 1)(22-1)" 2n 4 7n +4 sin(3n) (6 pts) Match each of the following with the correct statement. A. The series is absolutely convergent. C. The series converges, but is not absolutely convergent. D. The series diverges Vn (n + 1)(22-1)" 2n 4 7n +4 sin(3n)
Question 2 (12 marks) (a) Consider the sequence with terms 2n3 5"5 log n , n = 1,2,3,.... an 13 n8n (i) Determine whether {an} converges or diverges. If the sequence converges, find its lmit (ii) Determine whether diverges. Justify your answer an COnverges or n-1 (b) Consider the series (2n)! 2" (n!)? n=1 and determine whether it converges or diverges. Justify your answer Question 2 (12 marks) (a) Consider the sequence with terms 2n3 5"5 log n , n...