Definition:Divergent Sequence

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This page is about divergent sequences. For other uses, see Divergent (Analysis).

Definition

A sequence which is not convergent is divergent.


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Examples

Example: $\paren {\dfrac 2 3 + \dfrac {3 i} 4}^n$

Let $\sequence {z_n}$ be the complex sequence defined as:

$z_n = \paren {\dfrac 2 3 + \dfrac {3 i} 4}^n$

Then $\ds \lim_{n \mathop \to \infty} z_n$ does not exist.


Example: $\paren {-1}^n + \dfrac i n$

Let $\sequence {z_n}$ be the complex sequence defined as:

$z_n \paren {-1}^n + \dfrac i n$

Then $\ds \lim_{n \mathop \to \infty} z_n$ does not exist.


Example: $i^n$

Let $\sequence {z_n}$ be the complex sequence defined as:

$z_n = i^n$

Then $\ds \lim_{n \mathop \to \infty} z_n$ does not exist.


Also see

  • Results about divergent sequences can be found here.


Sources

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