Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

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

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Clayton Craig

Numerade Educator

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

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 3

The Integral Test and Estimates of Sums

Sequences

Series

Oregon State University

Harvey Mudd College

Baylor University

Boston College

Lectures

01:59

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.

02:28

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.

01:10

Determine whether the seri…

02:17

06:39

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.

View More Answers From This Book

Find Another Textbook

06:30

3. A farmer wants to make a rectangular pen that encloses a total area of 21…

01:40

2, In & box, there are 8 red, 7 blue and 6 green balls, One ball is Pick…

05:07

A credit card company monitors cardholder transaction habits to detect any u…

05:06

Consider the following equation. 4x2 _ y2 = 5 (a) Find y by implicit differe…

01:24

BOTTOM LINE QUESTION: Suppose a 15 foot ladder is leaning on a vertical wa…

01:08

12. Solve the equationpta each )25-1 = 6logs(1 + 6) = 3

08:00

1. The integral fre"= d can be evaluated using 04. Integration by parts…

02:04

An economiat reports tha: 248 Ou: Qi = camce B00 mladle-Income American nous…