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 converges or diverge…

03:14

Question

Answered step-by-step

Problem 7 Easy Difficulty

Determine whether the series converges or diverges.
$ \displaystyle \sum_{n = 1}^{\infty} \frac {9^n}{3 + 10^n} $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Mary Wakumoto
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Mary Wakumoto

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

01:04

Yiming Zhang

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 4

The Comparison Tests

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

01:01

Determine whether the seri…

02:08

Determine whether the seri…

03:47

Determine whether the seri…

03:30

Determine whether the seri…

00:58

Determine whether the seri…

01:35

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

All right. We want to see if this series converges. So one way to test it is do the ratio test and the ratio test says that if I take the limit as N goes to infinity of the next term over the current term and take absolute value of that. If we get less than one then the series converges And a seven is just this portion. Okay, so let's set it up for us and um let's go do that. So let's do the limit As and goes to infinity of our next term. Our next term is nine To the n plus one over three plus 10 to the N plus one. Who all over 9 to the end, three Plus 10 to the end. So we've got that over that. Alright, so let's kind of do like terms next to each other. So we can really compute the limit. So we'll do the nine to the n plus 1/9 to the end. And then uh we can take the three plus 10 to the end, that's on the very bottom. That flips to the top over three plus 10 to the n plus one. Okay, so the left part we can subtract exponents. So we will get limit as N goes to infinity of nine to the end plus 1/9 to the end. Well that's I can subtract exponents. So N plus one minus 10. So I just get I just get nine for that term. Now the other term before we look at it, Notice that we're going to infinity. So this term of three compared to 10 p.m. It's going to become trivially small. So we can approximate those at zero when we're approaching infinity. Therefore I can then also look at the exponents. Um 10 to the end minus. Uh Well it's 10 to the end over 10 to the n plus one. So one way to look at it is I have an extra 10 on the bottom. So I can divide by 10 here. Uh and notice that that is equal to 9/10. That is less than one. Therefore the series converges. Yay, so are serious converges. There are other ways to um saw this like the direct comparison test but but this way definitely works. So um All right. I have a wonderful day and enjoy everything you're doing after the video. All right. Take care.

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
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

01:01

Determine whether the series converges or diverges. $\sum_{n=1}^{x} \frac{n^{n}…

02:08

Determine whether the series converges or diverges. $\sum_{n=1}^{\infty} \frac{…

03:47

Determine whether the series converges or diverges. $ \displaystyle \sum_{n = …

03:30

Determine whether the series converges or diverges. $ \displaystyle\sum_{n = 1…

00:58

Determine whether the series converges or diverges. $ \displaystyle \sum_{n = …

01:35

Determine whether the series converges or diverges. $\sum_{n=1}^{\infty} \frac{…
Additional Mathematics Questions

03:00

The question is under the topic differential calculus.An environmental stud…

05:51

Q1 : y''' - 6y'' + 11y' - 6y = 0 differential …

02:09

A capacitor with a capacitance of 5.0 coulombs/volt holds an initial charge …

03:57

In a piece of burned wood, it was found that 85.5% of carbon has decayed.Wha…

02:26

A family has two cars. The first car has a fuel efficiency of 35 miles per …

01:57

Explain the difference between simple interest and compound interest. Provid…

02:10

The cost in dollars to produce x cups of lemonade is represented by the func…

02:20

A ball is thrown from an initial height of 3 feet with an initial upward vel…

01:37

Determine whether ⊂, ⊆, both, or neither can be placed in the blank to make …

02:07

This question is under rational expressions.The time, t, to travel a distanc…

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