Math 2.0

Sequences, series, summability Concept

Algebra of limits

Builds on Limit of a sequence

Summary

The algebra of limits is a set of rules for limits of convergent sequences. The rules give the limit of a sum, a product or a quotient from the limits of the parts. If an→aa_n \to a and bn→bb_n \to b, then an+bn→a+ba_n + b_n \to a + b, anbn→aba_n b_n \to a b, and an/bn→a/ba_n / b_n \to a / b when b≠0b \ne 0. These rules let us find many limits from a few known ones.

Remarks

The rules are the nodes limit of a sum of sequences, limit of a product of sequences and limit of a quotient of sequences. Similar rules hold for the limit of a function.

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

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Sequence, definition, no evidence levelSequencedefinitionReal sequence, definition, no evidence levelReal sequencedefinitionLimit of a sequence, definition, no evidence levelLimit of a sequencedefinitionAlgebra of limits, concept, no evidence levelAlgebra of limitsconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Sequence definition
  2. Real sequence definition
  3. Limit of a sequence definition
  4. Algebra of limits concept

Further reading

  1. Web https://en.wikipedia.org/wiki/Limit_of_a_sequence, Properties
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Aliaseslimit-laws
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MSC40A05
UsesLimit of a sequence

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