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Compute sup,inf, and more

  • Thread starter *melinda*
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  • #1
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Question:
(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:
 

Answers and Replies

  • #2
1,444
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.
 
  • #3
86
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So that would mean that my inf = -1, just like I thought it should be. :rolleyes:

Thanks a lot!
 

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