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

Use the Ratio Test to determine whether the serie…

03:36

Question

Answered step-by-step

Problem 22 Medium Difficulty

Use the Ratio Test to determine whether the series is convergent or divergent.

$ \frac {2}{3} + \frac {2 \cdot 5}{3 \cdot 5} + \frac {2 \cdot 5 \cdot 8}{3 \cdot 5 \cdot 7} + \frac {2 \cdot 5 \cdot 8 \cdot 11}{3 \cdot 5 \cdot 7 \cdot 9} + \cdot \cdot \cdot $


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
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor University

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

04:03

Use the Ratio Test to dete…

01:40

Determine whether the seri…

05:04

Use the Ratio Test to dete…

02:47

$7-24$ Use the Ratio Test …

05:31

Determine whether the seri…

02:59

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

to use the ratio test here. It would be helpful tohave the formula for the end term of the theories. Now we see here are first term a one a two and so on. And if we keep going on in this pattern you see in the numerator we start off with two and then we keep adding three. So it looks like we should have three and minus one. And you can check if an equals one. You too. If any calls to you get five and each time and increases the new writer and includes an additional factor of three increases by three. Now in the denominator, you see that we have three, five and so on and in the denominator or increasing by two. So this time we should have ah too, and and there instead. But when we plug in n equals one, we'd like to get three. So we should do two and plus one. So here's our formula for the INSERM. And so now we go to the ratio test This we look at the limit and goes to infinity and plus one over. And so now I could drop the absolute values because all of our numbers were positive. And now here, let's do a and plus one. So the numerator over here and then we would keep multiplying. And then we would include the next term. So that's the numerator for an plus one, Sol Do listen blue and the denominator and then we increase and buy one and I will divide buy n So we'Ll just use our formula here and now, as usual will go ahead and take that denominator flip it upside down and multiply it. So here, running out of a bit of room here. So let's see if we could squeeze this in and notice the very last term over here. If you simplify this, that's three n plus two in the denominator and then the very last term here, that's a two one plus three. No. Okay, now we're multiplying this by this thing after we flip it upside out and that will start canceling out as much as we can. So we look at the denominator over here and you see that you could cancel all the terms except the last one with this numerator over here. So that leaves us with a to N plus three. And the denominator. How about the numerator? It looks like we could cancel and then here. Sorry. That should have been a five. It looks like you could cancel everything up to three and minus one, and then you're left with to re n plus two. At this point, if it helps, you can use local tells rule toe, evaluate that limit. In either case, you get three over to which is bigger than one. So the Siri's diverges by the ratio test.

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
178
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
75
Hosted by: Alonso M
See More

Related Topics

Sequences

Series

Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor University

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

04:03

Use the Ratio Test to determine whether the series is convergent or divergent. …

01:40

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

05:04

Use the Ratio Test to determine whether the series is convergent or divergent. …

02:47

$7-24$ Use the Ratio Test to determine whether the series is convergent or div…

05:31

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

02:59

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

01:58

Graphing Linear Inequality in Two Variables
Inatructions: Using a graphin…

02:48

Find the perimeter of AUVW . Round your answer to the nearest tenth if neces…

04:23

23 - 24. Given the figure below, the relationships among chords, arcs, centr…

01:18

Select tne correct answer:
Chase is constructing equilateral triangle EFG…

02:56

A B and €C are three similar solids
The surface area of A is 24cm? The su…

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