Download the App!

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

Determine whether the series is convergent or divergent.$ \displaystyle \sum_{n = 1}^{\infty} \frac {n^3}{n^4 + 4} $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

divergent

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 3

The Integral Test and Estimates of Sums

Sequences

Series

Missouri State University

Baylor University

Idaho State 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…

01:02

01:58

01:48

this problem. We want to determine if the Siri's converges or diverges, so we'll use an integral again. We're just gonna have to change what's inside of it. It will be from one to infinity, though, because the summation is from one to infinity. In this case, what we're gonna have is X cube over X to the fourth class four. What we see is this is undefined. So it's ultimately going to mean that the Siri's diverges on beacon figure out why this is the case. Because, um, what we see is, if we evaluate this inter rule, what will end up getting in the natural log? Because we have this done here, the fractional value. So when we get these natural logs on DWI evaluate, it will end up getting, um, an infinite value. So with that, we see that the integral evaluated at this is infinity. Andi, therefore, we know that the integral diverges, um, and since the integral diverges, that tells us that the Serie ultimately diverges

View More Answers From This Book

Find Another Textbook

02:57

CLcould terminate in given the value of the trigonometric function (Sele…

00:58

unte the foloning in tens of sin and cos 8; then amplity possible: (Leate ro…

01:04

Question 23 (2 points)What happens to the percentile ranks as one moves …

01:51

Ifthe test statistic is to with 6 degrees of freedom and 0= 0.025_ then the …

02:00

Use the Intermediate Value Theorem to show that there is root of the given e…

04:14

The revenue R (in dollars) from renting apartments can De modeled by R = 2x(…

Gz0[0=2 1 "(9) =9 Mt) = T6)h'()(a) h '(31(6} …

02:55

Solving trianglc with the Iaw ofi sines= Problem LypeConsidertriangl…

02:36

Watch the video and then solve the problem given below:Click here to wat…

03:09

Convert each decimal degree measure into degrees-minutes-seconds and each de…