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!

Compute sup,inf, and more

  1. Sep 17, 2005 #1
    (I've got a few like this, so I'd like to know if I am doing them correctly.)

    Compute the sup, inf, limsup, liminf, and all the limit points of the following sequence [itex]x_1, x_2,...[/itex] where

    [tex]x_n = 1/n + (-1)^n[/tex]

    What I did was write down the first few terms to get an idea of the behavior of the sequence.
    From this I found that the limit points were 1 and -1
    limsup = 1
    liminf = -1
    sup = 1.5 (I think)
    inf = 0 (I'm not sure)

    I'm not so sure about the inf because I don't think inf = liminf is allowed, but in this case the lower endpoint and the liminf both equal -1, I think...

    Did I determined these values by the correct method, or is there some formal way of which I am unaware to 'compute' these things?

    Also, are my values correct?

    thanks-a-bunch :smile:
  2. jcsd
  3. Sep 17, 2005 #2
    write out the first few terms of the sequence and watch the trend of the terms. Your inf is wrong. Your sup is fine.
  4. Sep 17, 2005 #3
    So that would mean that my inf = -1, just like I thought it should be. :rolleyes:

    Thanks a lot!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Compute sup,inf, and more
  1. Prove lim = inf(x) (Replies: 0)

  2. Lim sups and lim infs (Replies: 2)

  3. Moving a charge from inf (Replies: 10)