I am trying to find the cluster point of the sequence $a_{n}:=n+(-1)^nn$. Can you please check my solution?
The subsequence diverges for increasing even $n$ since $2n$ grows infinitely.
The subsequence converges to $0$ for increasing odd $n$ since $n+(-1)n=0$
So my conclusion is that there is only one cluster point and that is $0$.
Am I fine with this?