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[Solution Library] For each of the following statements determine if it is true or false. Every bounded sequence converges A convergent sequence positive numbers

Question: For each of the following statements determine if it is true or false.

  1. Every bounded sequence converges
  2. A convergent sequence positive numbers has a positive limit.
  3. The sequence \(\left\{ {{n}^{2}}+1 \right\}\) converges.
  4. A convergent sequence of rational numbers has a rational limit.
  5. The limit of a convergent sequence in the interval (a, b) also belongs to (a, b).

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