Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

Determine whether the series is absolutely conver…

07:46

Question

Answered step-by-step

Problem 5 Easy Difficulty

Determine whether the series is absolutely convergent or conditionally convergent.

$ \displaystyle \sum_{n = 1}^{\infty} \frac {\sin n}{n^2} $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

JH
J Hardin
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by J Hardin

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 6

Absolute Convergence and the Ratio and Root Tests

Related Topics

Sequences

Series

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Grace He
Catherine Ross

Missouri State University

Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:59

Series - Intro

In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence of real numbers is called a finite series. The sum of an infinite sequence of real numbers may or may not have a well-defined sum, and may or may not be equal to the limit of the sequence, if it exists. The study of the sums of infinite sequences is a major area in mathematics known as analysis.

Video Thumbnail

02:28

Sequences - Intro

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first "n" natural numbers (for a finite sequence). A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.

Join Course
Recommended Videos

01:39

Determine whether the seri…

04:46

Determine whether the seri…

00:53

Determine whether the seri…

00:49

Determine whether the seri…

01:07

Determine whether the seri…

03:49

Determine whether the seri…

03:27

Determine whether the seri…

01:09

Determine whether the seri…

00:45

Determine whether the seri…

04:25

Determine whether the seri…

Watch More Solved Questions in Chapter 11

Problem 1
Problem 2
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 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53

Video Transcript

let's go ahead and show that this Siri's is absolutely conversion. So to do that well we should be looking at is not the original Siri's, but the Siri's that you get after you take the absolute value of the terms that your adding. So this here is here and that I just wrote, If this is a convergence series, then the original serious conversions. So if this Siri's converges, then the original is absolutely conversion. Therefore, let's look at this. Siri's here. Now we have sign and over and square. Well, you know, Sign is always less than or equal to one an absolute value. So let's just go ahead and replace sign with one. So here we no sign of end, less than or equal to one that justifies this inequality over here. So we're using the comparison test Now. If we look at this, Siri's here. This Siri's convergence by the PT Test. So it's a Pee series with P equals two that's bigger than one. So it emerges. So by comparison, test Okay, this Siri's due to this inequality over here. That's why we're using comparison. This tells us that if we look at the Siri's of Signe and over and square absolute value from one to infinity that this also converges now going on to the next page. Therefore, we've just shown that the original Siri's from one to infinity sign in over and square that this is absolutely conversion, and that's our final answer.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
94
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
54
Hosted by: Alonso M
See More

Related Topics

Sequences

Series

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

Calculus 2 / BC Courses

Lectures

Video Thumbnail

01:59

Series - Intro

In mathematics, a series is, informally speaking, the sum of the terms of an infinite sequence. The sum of a finite sequence of real numbers is called a finite series. The sum of an infinite sequence of real numbers may or may not have a well-defined sum, and may or may not be equal to the limit of the sequence, if it exists. The study of the sums of infinite sequences is a major area in mathematics known as analysis.

Video Thumbnail

02:28

Sequences - Intro

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. Formally, a sequence can be defined as a function whose domain is either the set of the natural numbers (for infinite sequences) or the set of the first "n" natural numbers (for a finite sequence). A sequence can be thought of as a list of elements with a particular order. Sequences are useful in a number of mathematical disciplines for studying functions, spaces, and other mathematical structures using the convergence properties of sequences. In particular, sequences are the basis for series, which are important in differential equations and analysis. Sequences are also of interest in their own right and can be studied as patterns or puzzles, such as in the study of prime numbers.

Join Course
Recommended Videos

01:39

Determine whether the series is absolutely convergent, conditionally convergent…

04:46

Determine whether the series is absolutely convergent, conditionally convergent…

00:53

Determine whether the series is absolutely convergent, conditionally convergent…

00:49

Determine whether the series is absolutely convergent, conditionally convergent…

01:07

Determine whether the series is absolutely convergent, conditionally convergent…

03:49

Determine whether the series is absolutely convergent, conditionally convergent…

03:27

Determine whether the series is absolutely convergent, conditionally convergent…

01:09

Determine whether the series is absolutely convergent, conditionally convergent…

00:45

Determine whether the series is absolutely convergent, conditionally convergent…

04:25

Determine whether the series is absolutely convergent, conditionally convergent…
Additional Mathematics Questions

02:09

s. Find the product of sum of three consecutive smallest positive numbers wi…

03:46

1 divided by 11 1 divided by 11 decimal expansion

01:37

CAUTION: If you answer wrong, something tragic will happen.Gravitational for…

02:46

Find the coordinates of a point P, which lies on the line segment joining th…

01:27

write the first three terms of the Ap whose first term is root2 common diffe…

06:01

Construction of a building: Raman is a contractor; he is constructing a buil…

00:44

Construction of a building: Raman is a contractor; he is constructing a buil…

01:36

The day temperature on Moon can reach 130°C. At night the temperature can dr…

01:30

1. Bhumika bought 5/9 kg of flour. She repacked it equally into 15 packets.a…

01:04

subtract 25x-5x2 from 15x2 - 5x + 56 in row method

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started