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, to four decimal places, the first ten …

03:24

Question

Answered step-by-step

Problem 21 Medium Difficulty

Calculate, to four decimal places, the first ten terms of the sequence and use them to plot the graph of the sequence by hand. Does the sequence appear to have a limit? If so, calculate it. If not, explain why.
$ a_n = 1 + (- \frac {1}{2})^n $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Gabriel Rhodes
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Gabriel Rhodes

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 1

Sequences

Related Topics

Sequences

Series

Discussion

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

Missouri State University

Anna Marie Vagnozzi

Campbell University

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

05:15

Calculate, to four decimal…

03:24

Calculate, to four decimal…

03:19

Calculate, to four decimal…

04:44

Calculate, to four decimal…

03:05

Calculate, to four decimal…

04:33

Calculate, to four decimal…

03:30

Calculate, to four decimal…

07:30

Calculate, to four decimal…

04:07

Calculate, to four decimal…

07:47

Calculate, to four decimal…

09:02

$5-8$ Calculate, to four d…

04:37

Calculate, to four decimal…

04:26

Calculate, to four decimal…

03:28

$19-22$ Calculate, to four…

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
Problem 93

Video Transcript

the first few terms that we have here one half when we just plug in in equals one five over for when we're plugging in equals two and bunch of other terms. But it's more helpful. Tohave it written in decimal form zero point five one point two five Your point eight seven five one point o six two five zero point nine six eight Hey, one point o one five six zero point nine nine two two one point. Oh oh three nine your point nine nine eight Oh, one plant Oh, oh, no. Nine. Okay. And then Graff, these we label one through ten down here and then of our values get above one point two five. So we'LL just stop up here at one point two five. So for one, we have zero point five for two. We have one point two five for three. We have zero point eight seven five for four. We have one point o six two five for five for n equals five, we have zero point nine six eight eight for what sees we're on in equal six Now for an equal six, we have one point o one five six okay. And you, Khun, you can start to see that we're reaching some horizontal Assam towed here. All right. These dots are going to be getting closer and closer to this horizontal ask himto so it it does appear that we converge. Okay, it looks like we're converging toe one. And if we write the limit as n goes to infinity of a n, we see that, Yeah, we do end up getting one. Because as n goes to infinity, minus one half to the end is going to go to zero because one half is less than one an absolute value. So if you keep multiplying it by itself, then it's going to approach zero.

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
162
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
70
Hosted by: Alonso M
See More

Related Topics

Sequences

Series

Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

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

05:15

Calculate, to four decimal places, the first ten terms of the sequence and use …

03:24

Calculate, to four decimal places, the first ten terms of the sequence and use …

03:19

Calculate, to four decimal places, the first ten terms of the sequence and use …

04:44

Calculate, to four decimal places, the first ten terms of the sequence and use …

03:05

Calculate, to four decimal places, the first ten terms of the sequence and use …

04:33

Calculate, to four decimal places, the first ten terms of the sequence and use …

03:30

Calculate, to four decimal places, the first ten terms of the sequence and use …

07:30

Calculate, to four decimal places, the first ten terms of the sequence and use …

04:07

Calculate, to four decimal places, the first ten terms of the sequence and use …

07:47

Calculate, to four decimal places, the first ten terms of the sequence and use …

09:02

$5-8$ Calculate, to four decimal places, the first ten terms of the sequence an…

04:37

Calculate, to four decimal places, the first ten terms of the sequence and use …

04:26

Calculate, to four decimal places, the first ten terms of the sequence and use …

03:28

$19-22$ Calculate, to four decimal places, the first ten terms of the sequence …
Additional Mathematics Questions

01:39

Let
u=3i-j,v=4i+j,w=i+4j Find the specified scalar:
(v+w)
(+w)-L

01:27

Cobalt-60 is a radioactive isotope of the element cobalt: It (t) = Aoe-0.131…

01:35

The 2013-2014 roster of the Seattle Seahawks, winners of the 2014 NFL Super …

02:56

The 2013-2014 roster of the Seattle Seahawks; Winners of the 2014 NFL Super …

02:27

17X 74 1 1 1 =(n] 3 U

01:37

standard Normal distribution that take values greater than 1.68. Use Table A…

02:09

(30 marks) High temperature in Biloxi, Mississippi on July 21_ denoted by th…

01:47

Sup, ; 3 Ji 8 4 (&:) 2 Coss ( 2

01:16

Of 380 randomly selected medical students, 21 said that they planned to work…

02:26

Find the vertices and locate the foci for the hyperbola whose equation is gi…

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