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Explain why the Integral Test can't be used to de…

01:17

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Problem 26 Easy Difficulty

Determine whether the series is convergent or divergent.
$ \displaystyle \sum_{n = 1}^{\infty} \frac {n}{n^4 + 1} $


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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

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Top Calculus 2 / BC Educators
Heather Zimmers

Oregon State University

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Harvey Mudd College

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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.

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Watch More Solved Questions in Chapter 11

Problem 1
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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
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Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
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Problem 42
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Problem 45
Problem 46

Video Transcript

for this problem really is the comparison to and over end of the fourth plus one. It's always going to be less than n over just end of the fourth, because end of the fourth plus one is greater than end of the fourth. So dividing by a larger number, build a smaller number of all but end over end of the fourth reduces to one over and cute. We know that the series one over and Cubed converges as it is a P series. So, by comparison, test if our larger limit is this convergent series or sort of our larger terms come from this convergent series. In smaller terms of what we started with, we have convergent by comparison.

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Calculus: Early Transcendentals

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Related Topics

Sequences

Series

Top Calculus 2 / BC Educators
Heather Zimmers

Oregon State University

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
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