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Let $\{a_n\}$ be a sequence of real numbers. Then $\underset{n \to \infty}{\lim} a_n$ exists if and only if

  1. $\underset{n \to \infty}{\lim} a_{2n}$ and $\underset{n \to \infty}{\lim} a_{2n+2}$ exists
  2. $\underset{n \to \infty}{\lim} a_{2n}$ and $\underset{n \to \infty}{\lim} a_{2n+1}$ exist
  3. $\underset{n \to \infty}{\lim} a_{2n}, \underset{n \to \infty}{\lim} a_{2n+1}$ and $\underset{n \to \infty}{\lim} a_{3n}$ exist
  4. none of the above
in Calculus
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