Divergent Sequence/Examples
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Examples of Divergent Sequence
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.