Category:Examples of Convergent Real Sequences
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This category contains examples of Convergent Real Sequence.
Let $\sequence {x_k}$ be a sequence in $\R$.
The sequence $\sequence {x_k}$ converges to the limit $l \in \R$ if and only if:
- $\forall \epsilon \in \R_{>0}: \exists N \in \R_{>0}: n > N \implies \size {x_n - l} < \epsilon$
where $\size x$ denotes the absolute value of $x$.
Subcategories
This category has the following 2 subcategories, out of 2 total.
Pages in category "Examples of Convergent Real Sequences"
The following 13 pages are in this category, out of 13 total.
C
- Convergent Real Sequence/Examples
- Convergent Real Sequence/Examples/1 plus Reciprocal of n
- Convergent Real Sequence/Examples/2 n^3 - 3 n over 5 n^3 + 4 n^2 - 2
- Convergent Real Sequence/Examples/Arithmetic Mean of Previous 2 Terms
- Convergent Real Sequence/Examples/Difference between Adjacent Terms Bounded by alpha^n
- Convergent Real Sequence/Examples/n^2 - 1 over n^2 + 1
- Convergent Real Sequence/Examples/n^3 + 5 n^2 + 2 over 2 n^3 + 9
- Convergent Real Sequence/Examples/Term is Geometric Mean of Preceding Two Terms
- Convergent Real Sequence/Examples/x (n+1) = k over 1 + x n
- Convergent Real Sequence/Examples/x (n+1) = x n^2 + k
- Convergent Real Sequence/Examples/x + x^n over 1 + x^n
- Convergent Real Sequence/Examples/x n = root x n-1 y n-1, 1 over y n = half (1 over x n + 1 over y n-1)