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k0 k8 k=1k¹¹ + 3 5 ln k k geometric series r> 1. Prove these fa and the Root Test. W series using the Dive 80. Two sine series De converge. Σsin 1/2 k Additional Exercise 81. Limit Comparise Limit Compariso a. 82-87. A glimpse ah determine the values 82. 85. 8 WI 8 WI ΣΕ k! k² 88. Infinite prod 8 denoted II k=1 {a₁, α₁ a 2,0 a. Show th: sequenc

k0 k8 k=1k¹¹ + 3 5 ln k k geometric series r> 1. Prove these fa and the Root Test. W series using the Dive 80. Two sine series De converge. Σsin 1/2 k Additional Exercise 81. Limit Comparise Limit Compariso a. 82-87. A glimpse ah determine the values 82. 85. 8 WI 8 WI ΣΕ k! k² 88. Infinite prod 8 denoted II k=1 {a₁, α₁ a 2,0 a. Show th: sequenc

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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help with problem 51, explain every step please, they want you to use test like comparison test, ratio test, integral test,..etc to deterime if this series is converged or diverged. Please write it on a paper and not typing the solutions.

κ <bk. If Σak diverges, then Σbk diverges. Ck <ak. If Σak converges, then Σb and the test of your choice to determine onverge. k2 2k2 + 1 48. Σ 34 Ο k k - 1)2k 46. Σ k= k *) K² 1 k=1 5* – 1 43. Σ 51. K 100 =y (k + 1)! 2k | ek - 1 54. Σ 1 Σ k=1 Vk3 k + 1 ΣΚ k=2 1 kl+p?P_> 0 Dk 5 ln k 18 8 11 57. Σκι + 3 geometric series r> 1. Prove these fa and the Root Test. W series using the Dive 80. Two sine series De converge. 1 a. Σsin k Additional Exercise 81. Limit Comparist Limit Compariso 82-87. A glimpse ah determine the values 82. Σ 85. k=1 k! k= k 88. Infinite prod k=1 denoted Π {αμαι από a. Show thi sequence
Transcribed Image Text:κ <bk. If Σak diverges, then Σbk diverges. Ck <ak. If Σak converges, then Σb and the test of your choice to determine onverge. k2 2k2 + 1 48. Σ 34 Ο k k - 1)2k 46. Σ k= k *) K² 1 k=1 5* – 1 43. Σ 51. K 100 =y (k + 1)! 2k | ek - 1 54. Σ 1 Σ k=1 Vk3 k + 1 ΣΚ k=2 1 kl+p?P_> 0 Dk 5 ln k 18 8 11 57. Σκι + 3 geometric series r> 1. Prove these fa and the Root Test. W series using the Dive 80. Two sine series De converge. 1 a. Σsin k Additional Exercise 81. Limit Comparist Limit Compariso 82-87. A glimpse ah determine the values 82. Σ 85. k=1 k! k= k 88. Infinite prod k=1 denoted Π {αμαι από a. Show thi sequence
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