an +1 an +1 an + 1 Recall the Ratio Test which states that, if is a series with nonzero terms, and lim < 1, then S un converges absolutely. If lim > 1, or lim = 00, then an an an n- 00 Sa, diverges. n:(-3x)" – 1 (n + 1) For any fixed value of x such that x + 0, let a, Then, (n + 1)(-3x)" an +1 n+ 2 lim = lim n(-3x)n - 1 n + 1 n00 an n 00 n + 1 (n + 1)(-3x)" . n + 2 lim n- 00 VO o! OOU U + x -1
an +1 an +1 an + 1 Recall the Ratio Test which states that, if is a series with nonzero terms, and lim < 1, then S un converges absolutely. If lim > 1, or lim = 00, then an an an n- 00 Sa, diverges. n:(-3x)" – 1 (n + 1) For any fixed value of x such that x + 0, let a, Then, (n + 1)(-3x)" an +1 n+ 2 lim = lim n(-3x)n - 1 n + 1 n00 an n 00 n + 1 (n + 1)(-3x)" . n + 2 lim n- 00 VO o! OOU U + x -1
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 26RE
Related questions
Question
Transcribed Image Text:an + 1
an + 1
an + 1
Recall the Ratio Test which states that, if Sa, is a series with nonzero terms, and lim
n> 00
< 1, then )a, converges absolutely. If lim
n> 00
> 1, or lim
= 0,
then
an
a
n
a
n> 00
E, diverges.
Ean
For any fixed value of x such that x # 0, let a,
n·(-3x)"
%D
(n + 1)
Then,
(n + 1)(-3x)"
an + 1
n + 2
lim
n→ 00
lim
a
in
n(-3x)" -
n> 00
n + 1
n + 1
(n + 1)(-3x)" .
lim
n> 00
n - 1
n + 2
in
Vi o!
3
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage