Corollary: Limit of N-th Roots

(related to Proposition: Rational Powers of Positive Numbers)

For any positive real number \(a > 0\), the limit of n-th roots equals \(1\), formally

\[\lim_{n\to\infty}\sqrt[n]a=1.\]

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