1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sequences and existence of limit

  1. Nov 12, 2012 #1
    1. The problem statement, all variables and given/known data

    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→∞



    2. Relevant equations



    3. The attempt at a solution

    no clue :(
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 12, 2012 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    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?
     
  4. Nov 12, 2012 #3

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Also, please write out the full problem. Writing "then [itex]\lim_{n\rightarrow +\infty} a_n[/itex]" is incomplete.
     
  5. Nov 12, 2012 #4
    oops, sorry.
    i'll write a new thread (properly)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Sequences and existence of limit
  1. Existence of sequences (Replies: 1)

  2. Limits and Sequences (Replies: 8)

  3. Limit of a Sequence (Replies: 1)

Loading...