$\limsup$ and $\liminf$ computations for a sequence of subsets $(A_n)_{n=1}^{\infty}$ differing depending on $n$ odd or even

Question

Define the sequence $(A_n)_{n=1}^{\infty}$of subsets of $\mathbb{R}$ by $$A_n = \begin{cases} [0, \frac{1}{n}], & n \text{ odd} \\ [0, n], & n \text{ even} \end{cases}\text{.}$$ Then $$\liminf_{n \to \infty}A_n=\bigcup_{n \in \mathbb{N}}\bigcap_{k \geq n}A_k = \bigcup_{n \in \mathbb{N}}\{0\} = \{0\}$$ and $$\limsup_{n \to \infty}A_n=\bigcap_{n \in \mathbb{N}}\bigcup_{k \geq n}A_k = \bigcup_{n \in \mathbb{N}}[0, \infty) = [0, \infty)\text{.}$$ Are my computations correct?