My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
February 17th, 2018, 09:21 AM   #1
Banned Camp
 
Joined: Dec 2017
From: Tel Aviv

Posts: 87
Thanks: 3

Convergence

Because of what this series is convergent?

http://img2.timg.co.il/forums/47/128...e118d6d5f3.png

Last edited by greg1313; February 17th, 2018 at 11:35 AM.
policer is offline  
 
February 17th, 2018, 09:33 AM   #2
Math Team
 
Joined: Jul 2011
From: Texas

Posts: 2,755
Thanks: 1405



as posted, this expression represents a sequence, not a series.

The sequence converges ...

$\displaystyle \lim_{n \to \infty} \bigg[1 + \dfrac{(-1)^n}{n}\bigg] = 1$


The series diverges ...

$\displaystyle \sum_{n=1}^\infty \bigg[1 + \dfrac{(-1)^n}{n}\bigg]$

... if the individual terms of a series (in other words, the terms of the series' underlying sequence) do not converge to zero, then the series must diverge. This is the nth term test for series divergence.
skeeter is offline  
February 17th, 2018, 09:39 AM   #3
Banned Camp
 
Joined: Dec 2017
From: Tel Aviv

Posts: 87
Thanks: 3

Sorry, I not understood.
What the difference between series to sequence?
Can you write in some word what the definition of these terms?
Thank...
policer is offline  
February 17th, 2018, 10:31 AM   #4
Senior Member
 
Joined: May 2016
From: USA

Posts: 1,038
Thanks: 423

Quote:
Originally Posted by policer View Post
Sorry, I not understood.
What the difference between series to sequence?
Can you write in some word what the definition of these terms?
Thank...
https://en.wikipedia.org/wiki/Sequence

Basically, a sequence defines an enumerated group of numbers.

Your formula may define the infinite sequence

$x_1 = 1 + \dfrac{-\ 1^1}{1} = 0.$

$x_2 = 1 + \dfrac{-\ 1^2}{2} = \dfrac{3}{2}.$

$x_3 = 1 + \dfrac{-\ 1^3}{3} = \dfrac{2}{3}.$

$x_4 = 1 + \dfrac{-\ 1^4}{4} = \dfrac{5}{4}.$

https://en.wikipedia.org/wiki/Series_(mathematics)

An infinite series is the sum of an infinite sequence.
JeffM1 is offline  
February 17th, 2018, 10:33 AM   #5
Banned Camp
 
Joined: Dec 2017
From: Tel Aviv

Posts: 87
Thanks: 3

Thanks, i don't know if your definitions are suffice to know the mattrials.
But, Now I "think" that I know the different.
policer is offline  
February 17th, 2018, 10:34 AM   #6
SDK
Senior Member
 
Joined: Sep 2016
From: USA

Posts: 382
Thanks: 205

Math Focus: Dynamical systems, analytic function theory, numerics
How can you ask about convergence of a sequence of series if you don't even know what they are? I think you need to spend more time reading and understanding and less time trying to finish homework as quickly as possible.
SDK is offline  
February 17th, 2018, 10:42 AM   #7
Banned Camp
 
Joined: Dec 2017
From: Tel Aviv

Posts: 87
Thanks: 3

I should listen to you. Nice.
I will take a break from math in the next days.
policer is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
conevergence, convergence



Thread Tools
Display Modes






Copyright © 2018 My Math Forum. All rights reserved.