Convergent Complex Series/Examples
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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.