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!

Liminf and limsup problem

  1. Mar 4, 2010 #1
    1. The problem statement, all variables and given/known data
    Find liminf(xn) and limsup(xn) for xn = n(1-(-1)^n)


    2. Relevant equations



    3. The attempt at a solution
    I'm not really getting liminf and limsup, but stumbled through the method in my textbook and got liminf=0, limsup doesn't exist.

    Is that right? I don't think I did it right. If it's wrong, I can type out my working (I'd just prefer not to since it's pretty late).
     
  2. jcsd
  3. Mar 4, 2010 #2
    You are correct. I fins the easiest definition of limsup to be:

    [tex]\limsup_{n\rightarrow \infty}=\lim_{n\rightarrow \infty}(\sup_{m\geq n}x_m)[/tex]

    That is: as n approaches infinity, look at all the "peaks" of the [tex]x_m[/tex] for [tex]m\geq n[/tex]. You are looking for the "last peak".

    In the case of this function, the peaks get larger and larger (they occur when n is odd), so the "last one" is infinity, ie. it doesn't exist.

    Similarly for liminf, the "troughs" of the function are all zero (when n is even), so the "last one" will also be zero.

    I don't know if this will help much...I remember also being very confused by liminf and limsup when I first came across them!
     
  4. Mar 4, 2010 #3
    It helped a lot, thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Liminf and limsup problem
  1. Limsup and LimInf (Replies: 3)

  2. Limsup and liminf (Replies: 6)

Loading...