Category:Examples of Convergent Complex Sequences
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This category contains examples of Convergent Complex Sequence.
Definition 1
Let $\sequence {z_k}$ be a sequence in $\C$.
$\sequence {z_k}$ converges to the limit $c \in \C$ if and only if:
- $\forall \epsilon \in \R_{>0}: \exists N \in \R: n > N \implies \cmod {z_n - c} < \epsilon$
where $\cmod z$ denotes the modulus of $z$.
Definition 2
Let $\sequence {z_k} = \sequence {x_k + i y_k}$ be a sequence in $\C$.
$\sequence {z_k}$ converges to the limit $c = a + i b$ if and only if both:
- $\forall \epsilon \in \R_{>0}: \exists N \in \R: n > N \implies \size {x_n - a} < \epsilon \text { and } \size {y_n - b} < \epsilon$
where $\size {x_n - a}$ denotes the absolute value of $x_n - a$.
Subcategories
This category has only the following subcategory.
S
Pages in category "Examples of Convergent Complex Sequences"
The following 8 pages are in this category, out of 8 total.
C
- Convergent Complex Sequence/Examples
- Convergent Complex Sequence/Examples/((1 + i n) over (1 + n))^3
- Convergent Complex Sequence/Examples/(1 over 2 + i 4 over 5)^n
- Convergent Complex Sequence/Examples/(3+in)^2 over n^2
- Convergent Complex Sequence/Examples/(cos pi over n + i sin pi over n)^2n+1
- Convergent Complex Sequence/Examples/(cos pi over n+1 + i sin pi over n+1)^n
- Convergent Complex Sequence/Examples/tan i n