2n + 2" • Series: Test: Limit Comparison Test Зп + 3п? n=1

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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Comparison Test! Given the series, states whether the test applies and if it does use the test to see if the series converges or diverges.

(a) If the given test can be applied to the given series, complete the following.
(i) Determine a comparator series that you could use with the given test.
(ii) Indicate whether or not the given series converges or diverges.
(b) If the test cannot be applied to the given series, give a short reason as to why not.
2n + 2"
• Series: >
Test: Limit Comparison Test
3n + 3n'
n=1
(a) If the Test Applies:
(i) Comparator:
(ii) Choose one: Converges / Diverges
(b) If the Test Does Not Apply, explain why:
Transcribed Image Text:(a) If the given test can be applied to the given series, complete the following. (i) Determine a comparator series that you could use with the given test. (ii) Indicate whether or not the given series converges or diverges. (b) If the test cannot be applied to the given series, give a short reason as to why not. 2n + 2" • Series: > Test: Limit Comparison Test 3n + 3n' n=1 (a) If the Test Applies: (i) Comparator: (ii) Choose one: Converges / Diverges (b) If the Test Does Not Apply, explain why:
Expert Solution
Step 1

It is given that 

n = 1 2n + 2n3n + 3n

Let an = 2n + 2n3n + 3n ,              bn = 2n3n

an 0,          bn>0  n

use limit caparison test 

limn anbn

limn 2n + 2n3n+ 3n x 3n2n

limn 2n2n+ 2n2n3n3n+3n3n = 0+10+1 =1 > 0

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