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

Calculate the first eight terms of the sequence o…

03:54

Question

Answered step-by-step

Problem 7 Medium Difficulty

Calculate the first eight terms of the sequence of partial sums correct to four decimal places. Does it appear that the series is convergent or divergent?
$ \displaystyle \sum_{n = 1}^{\infty} \sin 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
Grace He
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

01:45

Calculate the first eight …

03:54

Calculate the first eight …

04:41

Calculate the first eight …

04:48

Calculate the first eight …

02:42

Calculate the first eight …

04:36

Calculate the first eight …

02:41

Calculate the first eight …

09:23

Calculate the first eight …

03:22

Calculate the first eight …

01:34

5-8 Calculate the first ei…

02:02

5-8 Calculate the first ei…

01:33

5-8 Calculate the first ei…

00:56

5-8 Calculate the first ei…

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 the first aid terms of the sequence of partial songs. So that's S one as two as three. I have to write all these out because we will need all these and as a now, by definition, we know us and is just the sum of the terms and from your starting point. So in this case, a one all the way up to an now for us one, this is just the first term which is signed one. It's as two sign one plus sign, too, and so on and then sign a will go all the way up to sign of as they will go all the way to sign eight. Now we'LL go to the computer software to approximate each of these toe form decimal places as required. So the first one is just this some just one term here. So let's go ahead and find that sign of one says you can see the signal notation We're just adding from one toe one. So this is just sign of one, and then we have point eight four one five, so that would be our first term for the second. Now, this time I'LL come back and make sure that I add in two terms. So now this time you see the sum goes from one to two you have one seven five o a one point seven five o eight. Then we'LL go to three terms. This time we have one point eight nine one nine. Now we go to us for adding the first four terms a one a two, a three and a four. We get one point one three five one now going to five. Actually, add those first five terms will be able to see in our signal notation that we are adding up to five terms there and we get one seven, six two. Now we go to six but adding the first six terms of the Siri's and we have negative point one o three three now going to seven terms point five five three seven five five three seven after the decibel and then the very last term is when we add first aid, those will be able to see and our signal notation. We're adding the essay here. All elements we have won point five four three one. So let's recheck that one point five four three one. So this answers the first part of the question. This is the sequence as one through s eight and then we rounded off tow for decibels four points after the decibel. Now let's go to the second part of the question. Does it appear that this Siri's converge? Izzard averages. So if you look at the partial sums we jumped about point nine, then we increased a little bit history. Then we decreased decrease almost all by one, decreased a little more, became positive again increased by one. So hear this does not look like the limit will exist. And here it'll diverge. And the actual reason that diverges is that the limit of sign in is not equal to zero Khama. So it diverges. Bye, the diversions test. So this is why it's not surprising that the sequence of partial sums is acting wildly. And this is 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
63
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
42
Hosted by: Alonso M
See More

Related Topics

Sequences

Series

Top Calculus 2 / BC Educators
Grace He

Numerade Educator

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

01:45

Calculate the first eight terms of the sequence of partial sums correct to four…

03:54

Calculate the first eight terms of the sequence of partial sums correct to four…

04:41

Calculate the first eight terms of the sequence of partial sums correct to four…

04:48

Calculate the first eight terms of the sequence of partial sums correct to four…

02:42

Calculate the first eight terms of the sequence of partial sums correct to four…

04:36

Calculate the first eight terms of the sequence of partial sums correct to four…

02:41

Calculate the first eight terms of the sequence of partial sums correct to four…

09:23

Calculate the first eight terms of the sequence of partial sums correct to four…

03:22

Calculate the first eight terms of the sequence of partial sums correct to four…

01:34

5-8 Calculate the first eight terms of the sequence of partial sums correct to …

02:02

5-8 Calculate the first eight terms of the sequence of partial sums correct to …

01:33

5-8 Calculate the first eight terms of the sequence of partial sums correct to …

00:56

5-8 Calculate the first eight terms of the sequence of partial sums correct to …
Additional Mathematics Questions

04:55

Ok, so im brand new at trigonometry. If i have a right triangle with an acu…

03:12

What is a possible career can I pursue

01:15

In a certian lottery, 4 differnt numbers between 1 and 11 inclusive are draw…

00:43

How do I Factor the expression
a y - a^{6} y^{6} ?

01:24

A district mathematics test for all third graders had a normal distribution …

02:26

1. Two roommates, roommate A and roommate B, are about to go cruising with a…

01:52

a farmer has a triangular garden with two sides at right angles and the thir…

03:05

In the Federal Trade Commission (FTC) Price Check" study of electronic …

03:24

a flagpole 25 feet tall stands on a top of a building. from a point in the s…

01:26

The maximum temperature on Thursday was 18 degree celsius.On Friday it incre…

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
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started