If (an)n is a sequence of positive real numbers that converges to 0, then the series Σan/√n converges. a. False, here is a counter-example: an = 1/n. b. True, because (an)neN is bounded (since it converges) and thus an/√n →0 by ALT. c. True, because an/√n →0 by ALT and thus, by n-th term test, an/√n converges. d. False, here is a counter-example: an = 1/√√n.
If (an)n is a sequence of positive real numbers that converges to 0, then the series Σan/√n converges. a. False, here is a counter-example: an = 1/n. b. True, because (an)neN is bounded (since it converges) and thus an/√n →0 by ALT. c. True, because an/√n →0 by ALT and thus, by n-th term test, an/√n converges. d. False, here is a counter-example: an = 1/√√n.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 55E
Related questions
Question
100%
Need help with this question. Thank you :)
![If (an)n is a sequence of positive real numbers that converges to 0, then the series an/√n converges.
a. False, here is a counter-example: an
1/n.
b. True, because (an)neN is bounded (since it converges) and thus an/√n →0 by ALT.
c. True, because an/√n →0 by ALT and thus, by n-th term test, Σan/√n converges.
d. False, here is a counter-example: an = 1/√√n.
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe587adf5-17b3-4d31-bfe0-bfcde8e60070%2F07b43e8d-4a78-4db0-8d3c-e64b84668a49%2F4bha4vi_processed.png&w=3840&q=75)
Transcribed Image Text:If (an)n is a sequence of positive real numbers that converges to 0, then the series an/√n converges.
a. False, here is a counter-example: an
1/n.
b. True, because (an)neN is bounded (since it converges) and thus an/√n →0 by ALT.
c. True, because an/√n →0 by ALT and thus, by n-th term test, Σan/√n converges.
d. False, here is a counter-example: an = 1/√√n.
=
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781938168383/9781938168383_smallCoverImage.gif)
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
![College Algebra](https://www.bartleby.com/isbn_cover_images/9781938168383/9781938168383_smallCoverImage.gif)