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Show all relevant work in determining the convergence (absolute, conditional or divergence) k + 2 of the series (-1)*+1 ( ; k2 + k k=1 21(x + 1)* k2k Find the radius of convergence and interval of convergence of the following k=1

Show all relevant work in determining the convergence (absolute, conditional or divergence) k + 2 of the series (-1)*+1 ( ; k2 + k k=1 21(x + 1)* k2k Find the radius of convergence and interval of convergence of the following k=1

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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a) Show all relevant work in determining the convergence (absolute, conditional or divergence) k +2 of the series (-1)k+1 k2 + k k=1 b) 21(x + 1)* k2k Find the radius of convergence and interval of convergence of the following k=1 IM:
Transcribed Image Text:a) Show all relevant work in determining the convergence (absolute, conditional or divergence) k +2 of the series (-1)k+1 k2 + k k=1 b) 21(x + 1)* k2k Find the radius of convergence and interval of convergence of the following k=1 IM:
Expert Solution
Step 1

solution:- the given sequence is 

∑k=1∞(-1)k+1k+2k2+k here bn=k+2k2+k

 

 

Step 2

here we will use comparison test.

by comparison test

Suppose that we have two series  with for all n and  for all n. Then,

a) If  is convergent then so is .

b) If  is divergent then so is 

 

 

 

 

  

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