Divergent Series/Examples

Examples of Divergent Series

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

The complex series defined as:

$\ds S = \sum_{n \mathop = 1}^\infty \dfrac {n + i} {n^2}$

is divergent.

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

The complex series defined as:

$\ds S = \sum_{n \mathop = 1}^\infty \paren {\dfrac {2 + 3 i} {3 - 2 i} }^n$

is divergent.

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

The complex series defined as:

$\ds S = \sum_{n \mathop = 1}^\infty \dfrac n {n^2 + i}$

is divergent.

Example: $\dfrac {\sin i n} {n^2}$

The complex series defined as:

$\ds S = \sum_{n \mathop = 1}^\infty \dfrac {\sin i n} {n^2}$

is divergent.