Let $\langle a_n \rangle = \dfrac{(-1)^n}{1+n}$ be a sequence in $\mathbb R$.
Considering the limit point(s) of this sequence and the subsequences that converge to this point, I have two subsequences: $ a_{2k} = \frac{1}{1+2k} \to 0 \text{ and } a_{2k+1} = \frac{-1}{1+2k+1} \to 0 $
If the question asks for the limit points of the sequence, and a subsequence that converges to this limit point, do I leave out the second subsequence? I don't think I've missed a limit point, but it doesn't hurt to check.