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(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