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Proposition: Convergence Behavior of the Inverse of Sequence Members Tending to Zero
If $(a_n)_{n\in\mathbb N}$ is a real sequence of positive (or negative) real numbers tending to zero, i.e. with $\lim_{n\to\infty} a_n=0,$ then the real sequence $(1/a_n)_{n\in\mathbb N}$ is tending to infinity, i.e. either to $+\infty$ (if $a_n > 0$ for all $n$) or to $-\infty$ (if $a_n < 0$ for all $n$).
Table of Contents
Proofs: 1
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References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
