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Determine whether the series is convergent or divergent.$ \displaystyle \sum_{n = 2}^{\infty} \frac {1}{n \ln n} $

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Divergent

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 3

The Integral Test and Estimates of Sums

Sequences

Series

Missouri State University

Harvey Mudd College

University of Nottingham

Idaho State University

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.

01:06

Determine whether the seri…

02:22

06:39

to do this problem. We're going to use the integral test because we have a continuous positive, decreasing function on this interval. So you want to evaluate integral from two to infinity of one over X Alan X check and I'm going to use the U substitution u equals Ellen acts. It gives me to you one over x dx so conveniently we have these all in are integral. So this becomes integral from some new end points of one over you to you, which will become Helen of you from the whatever those endpoints ended up being. And when we replace our use with exes, we will get the natural log of the natural law Vex evaluated from two to twenty. So we need to take a limit to deal with that infinity easily enough. And when we write this difference, we'LL see well that convergence or diversions looks like now Ellen of that should be non ex Buddy two now Alan of Ellen of twos. Just some number. But Ellen of Ellen of tea Asti goes to infinity also goes to infinity. So we know that our Siri's is diversion because the girl is diversion

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