Sequences and existence of limit

Click For Summary

Homework Help Overview

The discussion revolves around a problem concerning the convergence of a bounded sequence, specifically analyzing the conditions under which the limit of the sequence exists based on given inequalities involving another sequence.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the necessity of providing a complete problem statement and the importance of definitions related to convergence and boundedness. Some suggest exploring numerical examples or referencing previous problems to aid understanding.

Discussion Status

The discussion is in an early stage, with participants prompting the original poster to clarify the problem and encouraging attempts to engage with the material. There is no explicit consensus yet, as the original poster has indicated a lack of understanding.

Contextual Notes

There is a noted requirement for the original poster to provide a complete statement of the problem to facilitate better assistance. Additionally, the thread may be subject to closure if attempts are not made to engage with the problem.

Felafel
Messages
170
Reaction score
0

Homework Statement



Let an be a bounded sequence and bn such that

the limit bn as n→∞ is b and

0<bn ≤ 1/2 (bn-1)

Prove that if:

an+1 ≥ an - bn,

then

lim an
n→∞



Homework Equations





The Attempt at a Solution



no clue :(
 
Physics news on Phys.org
Please provide an attempt or this thread will be locked.

It's not possible to have "no clue". There are always things you can do:

  • Write down the relevant definition such as convergence and bounded.
  • Find a numerical example.
  • What were some previous examples/problems where you had to show convergence, what were the steps you took there? Can you mimic those to an extent?
 
Also, please write out the full problem. Writing "then [itex]\lim_{n\rightarrow +\infty} a_n[/itex]" is incomplete.
 
oops, sorry.
i'll write a new thread (properly)
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 10 ·
Replies
10
Views
3K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
1K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
2
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K