◀ ▲ ▶Branches / Analysis / Proposition: Convergence Behavior of the Inverse of Sequence Members Tending to Infinity
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
Thank you to the contributors under CC BY-SA 4.0! 
- Github:
-
References
Bibliography
- Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983
