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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!
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