Processing math: 100%

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.

Proofs: 1


Thank you to the contributors under CC BY-SA 4.0!

Github:
bookofproofs


References

Bibliography

  1. Forster Otto: "Analysis 1, Differential- und Integralrechnung einer Veränderlichen", Vieweg Studium, 1983