Convergent Complex Series/Examples

Examples of Convergent Complex Series

Example: $\dfrac {\paren {-1}^n + i \cos n \theta} {n^2}$

The series $\ds \sum_{n \mathop = 1}^\infty a_n$, where:

$a_n = \dfrac {\paren {-1}^n + i \cos n \theta} {n^2}$

is convergent.

Example: $\dfrac 1 {n^2 - i n}$

The series $\ds \sum_{n \mathop = 1}^\infty a_n$, where:

$a_n = \dfrac 1 {n^2 - i n}$

is convergent.

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

The series $\ds \sum_{n \mathop = 1}^\infty a_n$, where:

$a_n = \dfrac {e^{i n} } {n^2}$

is convergent.

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

The series $\ds \sum_{n \mathop = 1}^\infty a_n$, where:

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

is convergent.