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 0Dk5 ln k1881157. Σκι + 3geometric seriesr> 1. Prove these faand the Root Test. Wseries using the Dive80. Two sine series Deconverge.1a. Σsin kAdditional Exercise81. Limit ComparistLimit Compariso82-87. A glimpse ahdetermine the values82. Σ85.k=1 k!k= k88. Infinite prodk=1denoted Π{αμαι απόa. Show thisequence

Answered: Image /qna-images/answer/69c239d4-ab29-46be-b426-f44d603412d8.jpg

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

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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Question

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

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