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Section: Theorems Regarding Limits Of Sequences

There are some theorems that hold for all convergent sequences. In this section, we will present some of these theorems.

Table of Contents

  1. Proposition: Uniqueness Of the Limit of a Sequence
  2. Proposition: Sum of Convergent Real Sequences
  3. Proposition: Difference of Convergent Real Sequences
  4. Proposition: Product of Convegent Real Sequences
  5. Proposition: Product of a Real Number and a Convergent Real Sequence
  6. Proposition: Quotient of Convergent Real Sequences
  7. Proposition: How Convergence Preserves the Order Relation of Sequence Members
  8. Proposition: How Convergence Preserves Upper and Lower Bounds For Sequence Members

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References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
  2. Modler, F.; Kreh, M.: "Tutorium Analysis 1 und Lineare Algebra 1", Springer Spektrum, 2018, 4th Edition