9 Nov 2021
Problem 30
Page 592
Section 8.4: Other Convergence Tests
Chapter 8: Infinite Sequences and Series
Textbook ExpertVerified Tutor
9 Nov 2021
Given information
Given alternate series 
Step-by-step explanation
Step 1.
Observe that a series 
is called absolutely convergent if the series of absolute values
is convergent.
Take the sequence of a partial fraction of the alternate series is 
Since 
Therefore 
Observe that here 
is a geometric series with 
Here, common ratio 
, so the is convergent
Hence, is absolutely convergent
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- Problem 1a
- Problem 1b
- Problem 1c
- Problem 2a
- Problem 2b
- Problem 2c
- Problem 3
- Problem 4
- Problem 5
- Problem 6
- Problem 7
- Problem 8
- Problem 9
- Problem 10
- Problem 11
- Problem 11b
- Problem 12
- Problem 13
- Problem 14
- Problem 15
- Problem 16
- Problem 17
- Problem 18
- Problem 19
- Problem 20
- Problem 21
- Problem 22
- Problem 23
- Problem 24
- Problem 25
- Problem 26
- Problem 27
- Problem 28
- Problem 29
- Problem 30
- Problem 31
- Problem 32
- Problem 33
- Problem 34
- Problem 35
- Problem 36
- Problem 37a
- Problem 37b
- Problem 37c
- Problem 37d
- Problem 38a
- Problem 38b
- Problem 38c
- Problem 39
- Problem 39b
- Problem 39b
- Problem 39c
- Problem 40
- Problem 41a
- Problem 41b
- Problem 42a
- Problem 42b