Textbook ExpertVerified Tutor
18 Nov 2021
Given information
We are given the series 
and we have to find the radius of convergence and interval of convergence.
Step-by-step explanation
Step 1.
In this case, let let 
, then we have the following:
So by the ratio test, the given series is convergent if 
and divergent if 
.
The conclusion is that the radius of convergence is 
and the interval of convergence is (-1, 1).
If 
, the series becomes
which converges by the Alternating series test.
If x=1, the series becomes
Which finally diverges because it is a p-series where 
So, finally, the interval of convergence is [-1,1]
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- Problem 1
- Problem 2a
- Problem 2b
- Problem 3
- Problem 4
- Problem 5
- Problem 6
- Problem 7
- Problem 8
- Problem 9
- Problem 10
- Problem 11
- 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 25a
- Problem 25b
- Problem 26a
- Problem 26b
- Problem 26c
- Problem 26d
- Problem 27
- Problem 28
- Problem 29a
- Problem 29b
- Problem 29c
- Problem 30a
- Problem 30b
- Problem 30c
- Problem 31
- Problem 32
- Problem 33
- Problem 34
- Problem 35
- Problem 36a
- Problem 36b
- Problem 36c