Real numbers/Convergent sequences/Rules/Fact

Rules for convergent sequences

Let and be convergent sequences. Then the following statements hold.

  1. The sequence is convergent, and

    holds.

  2. The sequence is convergent, and

    holds.

  3. For , we have
  4. Suppose that and for all . Then is also convergent, and

    holds.

  5. Suppose that and that for all . Then is also convergent, and

    holds.