Let $\{a_n\}$ be a sequence of real numbers. Then $\underset{n \to \infty}{\lim} a_n$ exists if and only if
- $\underset{n \to \infty}{\lim} a_{2n}$ and $\underset{n \to \infty}{\lim} a_{2n+2}$ exists
- $\underset{n \to \infty}{\lim} a_{2n}$ and $\underset{n \to \infty}{\lim} a_{2n+1}$ exist
- $\underset{n \to \infty}{\lim} a_{2n}, \underset{n \to \infty}{\lim} a_{2n+1}$ and $\underset{n \to \infty}{\lim} a_{3n}$ exist
- none of the above