My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 30th, 2016, 08:09 AM   #1
Member
 
Joined: Aug 2016
From: illinois

Posts: 46
Thanks: 0

Question Series Convergence

If you are using the integral test to find if a series is convergent or divergent, and find the integral converges to a negative number, does that mean the series still converges.
fivestar is offline  
 
October 30th, 2016, 08:24 AM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,502
Thanks: 2511

Math Focus: Mainly analysis and algebra
The integral test operates on positive, monotonic functions only (from memory). You should investigate the integral of $|f(x)|$ to see if the series is absolutely convergent.

Last edited by v8archie; October 30th, 2016 at 08:30 AM.
v8archie is offline  
October 31st, 2016, 08:21 AM   #3
Senior Member
 
Joined: Mar 2015
From: New Jersey

Posts: 1,603
Thanks: 115

Integral Test

Let f(x) be positive, continuous , and non-increasing for x$\displaystyle \geq$ N and a$\displaystyle _{n}$ =f(n) for n$\displaystyle \geq$N.
Then a$\displaystyle _{n}$ converges or diverges according as $\displaystyle \int_{N}^{\infty}$f(x)dx converges or diverges.
zylo is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
convergence, series



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Find the radius of convergence, and the interval of convergence, of the series. Johanovegas Calculus 2 January 23rd, 2016 02:34 PM
Convergence and Series Sum Luiz Real Analysis 1 May 10th, 2015 10:38 AM
Series Convergence Kreiger Real Analysis 5 April 19th, 2015 04:09 PM
convergence of series walter r Real Analysis 3 April 5th, 2014 09:50 PM
series convergence? aaron-math Calculus 4 February 20th, 2013 04:29 AM





Copyright © 2018 My Math Forum. All rights reserved.