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Proposition: Infinite Geometric Series
Let \(x\) be a real number with the absolute value \(|x| < 1\). Then the real infinite series, called the infinite geometric series,
\[\sum_{k=0}^\infty x^n\]
is convergent, and its limit is
\[\sum_{k=0}^\infty x^n=\frac{1}{1-x}.\]
Table of Contents
Proofs: 1
Mentioned in:
Examples: 1
Proofs: 2 3 4 5 6 7
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References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
