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ISI2017-MMA-16

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Let $(x_n)$ be a sequence of real numbers such that the subsequences $(x_{2n})$ and $(x_{3n})$ converge to limits $K$ and $L$ respectively. Then

  1. $(x_n)$ always converges
  2. if $K=L$, then $(x_n)$ converges
  3. $(x_n)$ may not converge, but $K=L$
  4. it is possible to have $K \neq L$
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