# Definition:Divergent Sequence

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

## Definition

A sequence which is not convergent is divergent.

## 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.