Math 2.0

Sequences, series, summability Definition

Divergent sequence

Builds on Convergent sequence

Definition

A real sequence (an)(a_n) is divergent if it is not a convergent sequence. Thus, for each real number LL, the sequence (an)(a_n) does not converge to LL.

Remarks

The sequence an=(−1)na_n = (-1)^n is divergent, and it is bounded. The sequence an=na_n = n is divergent, and it tends to infinity. Some texts say that a sequence that tends to +∞+\infty diverges to +∞+\infty. It is still divergent in the sense of this definition.

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Sequence, definition, no evidence levelSequencedefinitionReal sequence, definition, no evidence levelReal sequencedefinitionLimit of a sequence, definition, no evidence levelLimit of a sequencedefinitionConvergent sequence, definition, no evidence levelConvergent sequencedefinitionDivergent sequence, definition, no evidence levelDivergent sequencedefinition
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. Convergent sequence definition
  5. Divergent sequence definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Limit_of_a_sequence, Real numbers
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