1. Not finding help here? Sign up for a free 30min 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!

Limit question

  1. Oct 21, 2009 #1
    1. The problem statement, all variables and given/known data

    this is more of a question I had within a question... but here it is:

    Suppose [tex]s_{k} = s_{2k-1} + s_{2k}[/tex]

    is true and I know for a fact that s_2k has no limit.

    Would that imply that s_k has no limit as well? Or is that not enough?

    Thanks in advance.

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 21, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Not enough. Take s_k=(-1)^k.
     
  4. Oct 21, 2009 #3
    Actually, you've provided "too much"! See, the statement "If [tex]s_{2k}[/tex] has no limit, then neither does [tex]s_k[/tex]" is the contrapositive of "If [tex]s_k[/tex] has a limit, then so does [tex]s_{2k}[/tex]," the truth of which follows quite readily for all sequences from the definition of a sequence limit.


    But this doesn't satisfy the condition that [tex]s_{2k}[/tex] not converge.
     
  5. Oct 21, 2009 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Good point. You are right. If s_2k doesn't converge, s_k can't converge.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Limit question
  1. Limit question ! (Replies: 2)

  2. Limit question (Replies: 10)

  3. Limits question (Replies: 6)

  4. Limit question (Replies: 3)

  5. Limits question (Replies: 5)

Loading...