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 = 2}^{\infty} \frac {\ln n}{n^2} $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

diverges

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 3

The Integral Test and Estimates of Sums

Sequences

Series

Clayton Craig

January 13, 2018

There is a mistake late in the problem. The P-series test says that for P>1, the series is CONVERGENT, so the overall series converges, not diverges.

Missouri State University

Baylor University

University of Michigan - Ann Arbor

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…

01:57

06:39

for the sake of an easier explanation, I'm going to split this Siri's by taking its first term out explicitly. If we take out Alan of two over two squared and add that the rest of the Siri's No should not be three there, that should be an end. What this allows us to do is say, well, for n equals three and Greater Ellen of n is created one, since the defense greater than E we get that. What this means is that from n equals three to Infinity, Allen of End Over and Squared is actually gonna be strictly greater than just the same serious for one over and scored. And as we know frumpy Siri's we have won over and to the P and P is greater than one. Then we have a divergence, Siri's. So we end up with this divergent and this's some number. So comparison test tells us that if we have the Siri's greater than another Siri's, and that smaller Siri's converges bear diverges than the other serious de bridges as well. So in this case, are smaller. Siri's is this diversion one. So our other Siri's conclusion someone's here, Vergis

View More Answers From This Book

Find Another Textbook

Numerade Educator

A leak in a pool causes the height of the water to decrease by 0.25 foot ove…

01:42

A once-popular children's doll is slowly declining in popularity. The q…

01:55

Write a system of inequalities that defines a shaded region that looks like …

04:43

Your neighbor also has a swimming pool of the same shape as yours, but it is…

The formula for the area of a trapezoid is A = one-half (b Subscript 1 Basel…

01:08

You have $3 to spend on lip balm and hand sanitizer. The equation 1.5x + 2.5…

01:14

Given a Poisson random variable X, where the average number of successes occ…

01:23

A deliveryman moves 10 cartons from the sidewalk, along a 10-meter ramp to a…

01:20

Question Number 11 of 20 - 8th Grade MathJohanna rented a car. Rentals c…

00:36

Q. A professional chef has a cone shaped strainer with a diameter of 6 inche…