9 Nov 2021
Problem 43
Page 584
Section 8.3: The Integral and comparison Tests; Estimating Sums
Chapter 8: Infinite Sequences and Series
Textbook ExpertVerified Tutor
9 Nov 2021
Given information
Given information 
and 
is convergent
Check 
is convergent or not.
Step-by-step explanation
Step 1.
Given that is convergent, so 
.
Apply Limit comparison test, Let and 
be two series of positive real numbers and 
, where 
is a finite number and 
then either both series converge or both diverge.
Let 
, then
Let 
, therefore by L'Hospital rule.
which is finite and positive,
Thus, by limit comparison test converges as is convergent with positive terms
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- Problem 1
- Problem 2
- Problem 3a
- Problem 3b
- Problem 4a
- Problem 4b
- Problem 5
- Problem 6
- Problem 7
- Problem 8
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- Problem 31
- Problem 32a
- Problem 32b
- Problem 32c
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- Problem 33c
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- Problem 35
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- Problem 39b
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- Problem 41
- Problem 42
- Problem 43
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- Problem 45
- Problem 46