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

Find at least 10 partial sums of the series. Grap…

03:08

Question

Answered step-by-step

Problem 9 Easy Difficulty

Find at least 10 partial sums of the series. Graph both the sequence of terms and the sequence of partial sums on the same screen. Does it appear that the series is convergent or divergent? If it is convergent, find the sum. If it is divergent, explain why.
$ \displaystyle \sum_{n = 1}^{\infty} \frac {12}{(-5)^n} $


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 2

Series

Related Topics

Sequences

Series

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

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

03:08

Find at least 10 partial s…

04:29

Find at least 10 partial s…

05:44

Find at least 10 partial s…

07:14

Find at least 10 partial s…

07:39

Find at least 10 partial s…

02:37

Find at least 10 partial s…

01:30

$3-8$ Find at least 10 par…

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
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86
Problem 87
Problem 88
Problem 89
Problem 90
Problem 91
Problem 92

Video Transcript

let's find at least ten partial sums of the Siri's. So let's do that first. Well, go ahead and just find as one all the way of Kirsten. Now, as a shortcut, I've used Wolfram to find the cave partial some here and then we're taking Kate to be one all the way up to Capel's ten. So these ten values here in the second column, these Rs one as two three Asfour as five x six a seven as a as nine in s ten. So those air exactly not approximately the first ten sums. Now let's go to the second part saw going back. If you could just pause the screen here to record those values, then I move on to the next part of the question. Now let's grab both the sequence of terms. That's the end civil graft. These guys, so plugging in and equals once attend for an and then we'LL also graph as one to ask him and then we'LL answer the questions. Does it appear that the series is conversion or not? And then we'LL come back and actually find the sum if it is conversion. So now we have a graphing calculator So let me take us that back here. So here I have the sequence A M equals twelve over negative five to the end. So here in purple, this's the graph of the first ten terms. They're very small. There is and gets larger than negative. The denominator. It's very large. And then you could see that it's alternating because of the negative sign, and it looks like the terms were going closer to zero. Now we also have the graph of the partial sums below, and this is will be in a different color. This's in red, so if we scroll down here, we see the first ten terms. So the first value, the first coordinate, is the end value. And then the second corner is the partial, some So here. This's saying that when you add the first six terms, you get about approximately negative one point nine nine nine nine. So it does look like this Red Siri's is converging to negative, too, so let's go ahead and verify this. It looks like the answer is conversion, and let's prove that it is here. The Siri's is geometric, and if that's unclear, you could just go ahead and write the end as negative twelve times negative one over five to the end. So there we see that are our equals negative one over five. This is why income urges. Now let's use the formula for geometric series to find the sum. So the Somme, which I actually just write it out and signal notation from one to infinity, fall over negative five to the end. The formula says you take the first term in the series and then divided by one minus R. So in this case, the first term is negative, twelve over five, and then we divide that by one minus negative, one over five. So this is negative. Twelve over five over six over five, and after cancelling out, we see that that's equals negative, too. So the Siri's converges to negative, too. 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
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
Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

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

03:08

Find at least 10 partial sums of the series. Graph both the sequence of terms a…

04:29

Find at least 10 partial sums of the series. Graph both the sequence of terms a…

05:44

Find at least 10 partial sums of the series. Graph both the sequence of terms a…

07:14

Find at least 10 partial sums of the series. Graph both the sequence of terms a…

07:39

Find at least 10 partial sums of the series. Graph both the sequence of terms a…

02:37

Find at least 10 partial sums of the series. Graph both the sequence of terms a…

01:30

$3-8$ Find at least 10 partial sums of the series. Graph both the sequence of t…
Additional Mathematics Questions

01:28

'A two-inch-long grasshopper can jump & horizontal distance of 40 i…

01:45

'The equation of the tangent line to the curve y = x2 4x at the point w…

02:34

'Figure 4.6 shows the curves y = Vx,x= 9,y =0, and rectangle with its s…

01:22

'For every 4,240 strings of decorative lights manufactured at lighting …

02:28

'7. A triangle hag a side length of 3 inches and an area of 22 square i…

00:25

'The admission fee at an amusement park is $2.50 for children and $5.20…

02:07

'Find two positive numbers satisfying the given requirements_ The produ…

02:07

'Find two positive numbers satisfying the given requirements_ The produ…

04:18

'Assume that when adults with smartphones are randomly selected, 37% us…

02:28

'Refer to the table summarizing service times (seconds) of dinners at a…

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