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 sequence converges or diverges. If it converges, find the limit.$ a_n = \frac {3 + 5n^2}{n + n^2} $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

5 as $n \rightarrow \infty$. Converges

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 1

Sequences

Series

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

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 sequ…

05:31

02:49

04:09

to figure out whether or not this converges. We just need to figure out whether or not this limit exists. Okay, so we could do the trick where we divide the top and the bottom by the largest power of end that we see in the denominator. It's in this case we'd be dividing the top in the bottom. Bye. In squared, as in Goes to infinity three over and squared, goes to zero and one over and goes to zero as well. So we just have five over one, which is five. So it does converge and it converges two five.

View More Answers From This Book

Find Another Textbook

04:37

A farmer buys 3 cows, 2 pigs, and 4 hens from a man who has 6 cows, 5 pigs, …

01:34

Find the cost of fencing a circular garden of radius 5.6m if the rate of fen…

00:47

A dice is thrown 24 time how many times do you expect the number 4 be appear…

02:14

If BOY is coded as ZPC, then GIRL is coded as

01:46

) A sector has a radius 7cm and makes an angle of 90° , the perimeter is____…

02:29

A baker baked some cookies . He tried to pack them in boxes of 6,8 or 12 coo…

02:00

A cube is painted red, green and blue on oppsite faces. Now the cube is divi…

02:38

Sullivan enterprises had a sales margin of 5%, sales of $4,000,000, and inve…

As the owner of a small restaurant, you purchase 5 boxes of napkins for $75.…