Limit of a sequence in an interval, defined to be different at each boundary.

[tomelwood]

Homework Statement

I have to study the limit of a sequence which is defined as follows. I'm not looking for an answer, just a method of how to do it, or even what this notation means.

A_n = { ($$\frac{n^{2}}{3n^{3}+1}$$, $$\frac{4n^{2}}{n^{2}+1}$$ ] n even
A_n = { ($$\frac{n^{2}}{6n^{2}-4}$$, $$\frac{2n^{2}+3}{4n^{2}}$$ ] n odd

Study if the limit as n--> $$\infty$$ exists.

Homework Equations

It may not be very clear from the latex code, but the terms are both in semi closed intervals (__ , __ ] which is mainly what is confusing me!

The Attempt at a Solution

All I have done so far is find the limits of each of the four expressions, but this hasn't really helped. Any pointers would be useful, or an example of a similar question.
Thanks.

 

[micromass]

You seem to take the limit of sets... How have you defined this?

 

[tomelwood]

To be honest, I have never seen this notation before, so have really no idea what I am doing. Taking limits of each of the four expressions and seeing what they tended to seemed the only thing I could do. Is there a way to do this type of question??

 

[micromass]

well; all depends on how that limit is defined. Maybe you should check your course to see if there's nothing like that in there... and if you don't find anything, then I'm afrain that you don't have enough information to solve the question