My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum


Reply
 
LinkBack Thread Tools Display Modes
December 6th, 2010, 08:25 AM   #1
Newbie
 
Joined: Dec 2010

Posts: 7
Thanks: 0

Proof of recurrence sequence convergence

Let be a recurrence sequecnce such that:

(1) and are positive reals

(2) For we have .

Proof that is convergent.
natkoza is offline  
 
December 6th, 2010, 09:51 AM   #2
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 937

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Proof of recurrence sequence convergence

What happens when the sum is > 1? What happens when the sum is < 1?
CRGreathouse is offline  
December 6th, 2010, 02:20 PM   #3
Newbie
 
Joined: Dec 2010

Posts: 7
Thanks: 0

Re: Proof of recurrence sequence convergence

From such cases (if you are talking about denominator) follows estimation for the next element of our sequence and I dont see anything more.

I tried to divide it into two subsequences such that 1st is composed of elements greater then one, and 2nd consists of numbers lesser then one. After that if 1st was nonincreasingand 2nd nondecreasing (actually it requiers their convergance only) with some easy calculus I can show that they have a common limit.

My prove attempt distinguished eight cases (there cant be three elements in a row that belong into on of these subsequances) but some of them are troublesome or simply false (for example they may be monotonic only for enought big values).
natkoza is offline  
Reply

  My Math Forum > College Math Forum > Real Analysis

Tags
convergence, proof, recurrence, 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
Recurrence Relation of a Sequence JSimmonds49 Algebra 1 August 18th, 2013 06:54 PM
Proof of Convergence of a (recursive) sequence MageKnight Real Analysis 1 May 2nd, 2013 07:40 PM
Convergence of a recurrence relation Punch Calculus 3 July 1st, 2012 09:10 PM
proof recurrence riotsandravess Number Theory 2 November 22nd, 2010 10:49 PM
Sequence convergence proof zve5 Real Analysis 2 September 24th, 2008 03:32 PM





Copyright © 2017 My Math Forum. All rights reserved.