# Analysis Help: Limit Points

Armbru35
Hi, I am asked to find the limit points of the given set A

A={((-1)^n)(2n/(n-4))}

so far I think 0 is a limit point, but I can't figure out if there are any more than just that one.

I believe every point in A is an isolated point, and that this set is open because every point in A contains a neighborhood contained in the set.

Any suggestions would be helpful. Thanks!!

You are using the word "limit" very carelessly. The sequence 2n/(n-4) has limit 2. That means its "set of limit points" is {2}. The sequence $(-1)^n2n/(n-4)$ does not converge- it has no limit. It does have two convergent subsequences- taking only even indices, it converges to 2, taking only odd indicees it converges to -2. So its "set of limits points" (not "its limits") is {-2, 2}.