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…

02:02

Question

Answered step-by-step

Problem 23 Easy Difficulty

Determine whether the series is convergent or divergent.
$ \displaystyle \sum_{k = 1}^{\infty} ke^{-k} $


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.
Top Calculus 2 / BC Educators
Catherine Ross

Missouri State University

Anna Marie Vagnozzi

Campbell University

Kristen Karbon

University of Michigan - Ann Arbor

Michael Jacobsen

Idaho State University

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

02:02

Determine whether the seri…

0:00

Determine whether the seri…

00:34

Determine whether the seri…

00:38

Determine whether the seri…

00:27

Determine whether the seri…

00:54

Determine whether the seri…

00:48

Determine whether the seri…

01:00

Determine whether the seri…

0:00

Determine whether the seri…

00:57

Determine whether the seri…

00:38

Determine whether the seri…

01:11

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

Video Transcript

for this problem. We are going to use the ratio test and first I'm just going to simplify the ratio and then I'll take the limit. So we want to know is what does next term that is the K plus one term look like when it's divided by case turns. So I'm going to distribute on the numerator and split the fraction up so I can simplify things down. So I get Kay need the negative K minus one over K to the negative k. Let's eat the negative K minus one over. Okay, even negative K. Now the left hand side reduces to just mhm the negative one and the right hand side. It becomes each the negative one over K. Now, if we take the limit, this K goes to infinity of this we say that either the negative one over K goes to zero. And so we are left with just the two, the negative one and either the negative one is less than one. So the series is convergent 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
94
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
54
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

Kristen Karbon

University of Michigan - Ann Arbor

Michael Jacobsen

Idaho State University

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

02:02

Determine whether the series is convergent or divergent. $ \displaystyle \sum_…

0:00

Determine whether the series is convergent or divergent. $\sum_{k=1}^{\infty} …

00:34

Determine whether the series is convergent or divergent. $$\sum_{k=1}^{\infty}(…

00:38

Determine whether the series is convergent or divergent. $$\sum_{k=0}^{\infty}(…

00:27

Determine whether the series is convergent or divergent. $$\sum_{k=2}^{\infty}(…

00:54

Determine whether the series is convergent or divergent. $$\sum_{k=1}^{\infty} …

00:48

Determine whether the series is convergent or divergent. $$\sum_{k=0}^{\infty}(…

01:00

Determine whether the series is convergent or divergent. $$\sum_{k=2}^{\infty}(…

0:00

Determine whether the series is convergent or divergent. $\sum_{k=1}^{\infty} …

00:57

Determine whether the series is convergent or divergent. $$\sum_{k=1}^{\infty}(…

00:38

Determine whether the series is convergent or divergent. $$\sum_{k=1}^{\infty}(…

01:11

Determine whether the series is convergent or divergent. $$\sum_{k=1}^{\infty}(…
Additional Mathematics Questions

05:50

Q1
According to the US Census Bureau, the population of the
Arizona, …

01:50

The figure above shows the probability density function for the
random va…

09:36

2. Ann sells bracelets in her store. Currently, each bracelet
sells for $…

03:32

A committee of 4 is chosen from a group of 8 women and 7 men.
Determine t…

01:48

A dresser drawer contains one pair of socks of each of the
following colo…

02:45

A company has two factories that manufacture light bulbs.
Suppose that 55…

00:56

According to Brad, consumers claim to prefer the brand-name
products bett…

02:14

Find the exact coordinates of the point at 240◦ on a circle of
radius 7, …

02:04

Find the horizontal and vertical components of the
vector v: |v| =
3, …

04:59

1. The count in a bacteria culture was 300 after 15 minutes and
2000 afte…

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