My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

Thanks Tree1Thanks
  • 1 Post By zylo
LinkBack Thread Tools Display Modes
April 19th, 2017, 02:55 AM   #1
Joined: Apr 2014
From: Greece

Posts: 52
Thanks: 0

Proving that a sequence does not converge

I want to prove using the epsilon-n theorem that the sequence $\displaystyle b_{n}=(-1)^{n}$ does not converge. I know I should use proof by contradiction but it's not clear how to do so.

I want to know what is the correct format to write the proof, not the concept behind it. Can anyone please write the analytical proof like how someone should prove it in an exam? I would be grateful
Vaki is offline  
April 19th, 2017, 03:52 AM   #2
Math Team
Joined: Dec 2013
From: Colombia

Posts: 6,939
Thanks: 2265

Math Focus: Mainly analysis and algebra
You write it and I'll provide feedback. Hint: it is sufficient to demonstrate a value of epsilon for which we can't find a value of n.
v8archie is online now  
April 19th, 2017, 04:03 AM   #3
Math Team
Joined: Jan 2015
From: Alabama

Posts: 2,649
Thanks: 680

You can use the fact that this sequence has two subsequences that converge to 1 and -1 to give you an idea what values to use.
Country Boy is online now  
April 19th, 2017, 04:04 AM   #4
Joined: Apr 2014
From: Greece

Posts: 52
Thanks: 0

I know the concept behind it. And I also understand that all I have to do is to find a value for ε so that |bn-b|>= ε
What I don't know is how to write it in a mathematically correct way. That's why I asked for the solution so that I can have a basic format to work with on other proofs like this
Vaki is offline  
April 19th, 2017, 04:10 AM   #5
Senior Member
Joined: Mar 2015
From: New Jersey

Posts: 1,134
Thanks: 88

$\displaystyle |a_{n}-L|<\epsilon$, n>N

$\displaystyle -\epsilon<a_{n}-L<\epsilon$

$\displaystyle L-\epsilon<(-1)^{n}<L+\epsilon$

$\displaystyle L-\epsilon \geq 0$ can't be satisfied.

$\displaystyle L-\epsilon < 0 \rightarrow L+\epsilon < 2\epsilon$ can't be satisfied
Thanks from Vaki
zylo is offline  

  My Math Forum > College Math Forum > Calculus

converge, proving, sequence

Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
does the following sequence converge or not? srecko Calculus 14 November 5th, 2016 11:40 AM
Sequence does not converge to limit a illyo Real Analysis 1 March 15th, 2015 05:50 AM
proving a property of the fibonacci sequence juarez.asf Number Theory 14 April 29th, 2014 02:59 AM
proving if a sequence is bounded.. nappysnake Calculus 6 November 28th, 2011 01:39 PM
Does the Sequence Converge or Diverge? veronicak5678 Calculus 2 November 4th, 2008 09:18 AM

Copyright © 2017 My Math Forum. All rights reserved.