• Support PF! Buy your school textbooks, materials and every day products Here!

Sequences and existence of limit

  • Thread starter Felafel
  • Start date
  • #1
171
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 :(

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
22,097
3,282
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?
 
  • #3
22,097
3,282
Also, please write out the full problem. Writing "then [itex]\lim_{n\rightarrow +\infty} a_n[/itex]" is incomplete.
 
  • #4
171
0
oops, sorry.
i'll write a new thread (properly)
 

Related Threads on Sequences and existence of limit

  • Last Post
Replies
1
Views
981
Replies
17
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
2
Views
2K
Replies
3
Views
3K
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
1
Views
738
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
1
Views
789
  • Last Post
Replies
4
Views
1K
Top