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Proposition: Convergence Behavior of the Inverse of Sequence Members Tending to Infinity
If (a_n)_{n\in\mathbb N} is a real sequence tending to infinity (i.e. either +\infty or -\infty), then there exists an index N\in\mathbb N such that a_n\neq 0 for all n\ge N and the real sequence (1/a_n)_{n\in\mathbb N} is a convergent real sequence with \lim_{n\to\infty} \frac 1{a_n}=0.
Table of Contents
Proofs: 1
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References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983