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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?

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    Thanks Hurkyl, you are right2012-12-22

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