💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Like

Report

Determine whether the series converges or diverges.$ \displaystyle \sum_{n = 1}^{\infty} \frac {5 + 2n}{(1 + n^2)^2} $

converges

Calculus 2 / BC

Chapter 11

Infinite Sequences and Series

Section 4

The Comparison Tests

Sequences

Series

Missouri State University

University of Nottingham

Idaho State University

Boston College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

03:18

Determine whether the seri…

03:14

02:15

03:30

03:56

03:51

02:47

03:20

02:49

00:44

you can use either the comparison test here or the limit comparison here. Let's just try using the usual that direct comparison test. So this Siri's right here. I couldn't replace this well first, though, actually, let me just keep it as an equal sign. Let me just go to that denominator first and simplify that. So I just have If I just foil that all out, I have to and square plus one plus into the fourth. Now, I could replace this with First of all, let me make the numerator larger. So I know that five is less than or equal to five in. So I'LL just call this five and plus two one and that's up. So if you make a numerator larger, the fraction is a whole good, larger And not only that, I'LL go ahead and make the denominator even smaller by just keeping the large term into the fourth. So here one plus two and swear plus and fourth is bigger than and to the fourth. So I made my denominator smaller and that also makes the fraction is a hole bigger. Therefore, this is why I'm allowed to just use replaced the previous series with the new series, as long as I'm using this inequality. Now let's go ahead and simplify that and equals one to infinity. That gives us seven n over into the fourth. And then you could go ahead and cross off one of those ends on topping on bottom. Your luck with three over on the bottom, and then we just have seven over in cubed. And now this is a P Siri's. So this converges by the Peters with in our case, P equals three. In any time P is larger than one, you always will have conversions. Therefore, also, we should make another observation that we're dealing with positive terms. Therefore, since we're dealing with positive terms, our series converges. Let's not write our let's actually just right the Siri's and equals one to infinity five plus two in all over one plus and swear square converges by the computer sent test, and that's your final answer

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

Determine whether the series converges or diverges.$ \displaystyle \sum_…

Determine whether the series converges or diverges.$ \displaystyle\sum_{…