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 convergent or div…

00:49

Question

Answered step-by-step

Problem 13 Medium Difficulty

Determine whether the series is convergent or divergent.
$ \frac {1}{3} + \frac {1}{7} + \frac {1}{11} + \frac {1}{15} + \frac {1}{19} + \cdot \cdot \cdot $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Clayton Craig
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Clayton Craig

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 3

The Integral Test and Estimates of Sums

Related Topics

Sequences

Series

Discussion

You must be signed in to discuss.
GM

Ghasan M.

December 15, 2022

I think it is 1/4x-1

Top Calculus 2 / BC Educators
Grace He
Catherine Ross

Missouri State University

Samuel Hannah

University of Nottingham

Joseph Lentino

Boston College

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

05:31

Determine whether the seri…

01:15

Determine whether the seri…

02:19

Determine whether the seri…

01:35

Determine whether the seri…

01:03

$9-26$ Determine whether t…

01:59

Determine whether the seri…

01:40

Determine whether the seri…

00:45

$9-26$ Determine whether t…

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

Video Transcript

since this is a continuous positive, decreasing function on the interval from one to infinity, we will use the integral test realizing their Siri's is one over to end plus one. So we will evaluate the integral from one to infinity of one over two X plus one suspect x, which means we have to take a limit. Uh, t ghost Infinity from wonder t of that function. And to integrate this we'LL do a u substitution Ah, where we will just have you equal to two x plus one which makes our do equal to two d x or in other words, one half to you is equal to the ex. So when we make our substitution, get the limit as T goes to infinity groom from some some coordinates here Andi won over you do you times one half We'LL take the one half hour in the front one half Really? We take the one half into the front of the integral. However property of limits is you can take constant coefficients in front limit as well. So just do it here for simplicity And when we integrate, we end up with the natural log of you evaluated from whatever those end points are. When we replace our exes back for youse, they will get one half the limit is he goes to infinity. Ah, Ellen. Two tea plus one minus Ellen of one. No, this whole difference in so gloomy. Ah, in between. In between these two steps I replaced the you with two x plus one from before and then plugged in the tea in the one from before. And as t goes to infinity Ah, Ellen to t plus one goes to infinity. So this whole, uh hola, mate goes to infinity. So because one half limit as t to infinity of the line of to t plus one minus on the one which is really just hero, that goes to infinity. So the siri's this diversion.

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
180
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
79
Hosted by: Alonso M
See More

Related Topics

Sequences

Series

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

Catherine Ross

Missouri State University

Samuel Hannah

University of Nottingham

Joseph Lentino

Boston College

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

05:31

Determine whether the series is convergent or divergent. $ \frac {1}{5} + \fra…

01:15

Determine whether the series is convergent or divergent. If it is convergent, f…

02:19

Determine whether the series is convergent or divergent. If it is convergent, f…

01:35

Determine whether the series is convergent or divergent. $$1+\frac{1}{3}+\fra…

01:03

$9-26$ Determine whether the series is convergent or divergent. $$ \frac{1}{3…

01:59

Determine whether the series is convergent or divergent. $$\frac{1}{5}+\frac{…

01:40

Determine whether the series is convergent or divergent. If it is convergent, f…

00:45

$9-26$ Determine whether the series is convergent or divergent. $$\frac{1}{5}+…
Additional Mathematics Questions

02:03

Solve V3 + 5 sin t =3 sin t for 0 < t 2t
Enter you answers as a comma …

02:09

Find the area of the shaded regions 20. 1 3 6 ft
Area

04:21

Suppose that y is a differentiable function of the variable I. Find Dry O y&…

01:23

Q#1
In a construction site, there are 4 excavators Each one must be alloc…

03:55

Consider the Markov chain whose transition probability matrix is given by (a…

03:34

Evaluate the derivatives of the given function for the given value of x Chec…

03:22

An engineer is planning t0 use gabion retaining wall t0 protect a section of…

05:44

Extending 13. Two roads intersect at 347 Two cars leave the intersection on …

02:27

Claire is a mechanical engineer working on the design of a new make of car T…

03:38

A telephone survey measured the percentage of students in ABC town who watch…

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