MHB Finding Cluster Points/Accumulation Points

[brooklysuse]

Find the set of cluster points for the set A := {(−1)n/n : n ∈ N}. Justify your answer with
proof.

I believe 0 is a cluster point but I can't figure out how to prove this, or how to prove any other point is not.

Any quick help would be appreciated. Thanks.

 

[Evgeny.Makarov]

Find the set of cluster points for the set A := {(−1)n/n : n ∈ N}.
I believe 0 is a cluster point

Hmm, I believe $$\frac{(-1)n}{n}=-1$$.

 

[Opalg]

Find the set of cluster points for the set A := {(−1)n/n : n ∈ N}. Justify your answer with
proof.

I believe 0 is a cluster point but I can't figure out how to prove this, or how to prove any other point is not.

Any quick help would be appreciated. Thanks.

I guess you mean $A := \{(−1)^n/n : n \in \Bbb{N}\}$. You are correct that $0$ is the only cluster point. To prove it, you will need to use the definition of a cluster point, which is ... ? (Start from there.)