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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.

| | | | created: 2020-07-10 19:47:15 | modified: 2020-07-10 19:49:36 | by: bookofproofs | references: [581], [8311]

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

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)

[581] Forster Otto: “Analysis 1, Differential- und Integralrechnung einer Veränderlichen”, Vieweg Studium, 1983

[8311] Modler, F.; Kreh, M.: “Tutorium Analysis 1 und Lineare Algebra 1”, Springer Spektrum, 2018, 4. Auflage