limit of nth root of n
The th root (http://planetmath.org/NthRoot) of tends to 1 as tends to infinity, i.e. the real number sequence
converges to the limit
(1) |
Proof. If we denote , we may write by the binomial theorem that
This implies, since all hand side are positive (when ), that
whence . Accordingly,
Q.E.D.
Note. (1) follows also from the corollary 3 in the entry growth of exponential function.
Title | limit of nth root of n |
---|---|
Canonical name | LimitOfNthRootOfN |
Date of creation | 2014-09-28 13:20:59 |
Last modified on | 2014-09-28 13:20:59 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 8 |
Author | pahio (2872) |
Entry type | Example |
Classification | msc 12D99 |
Classification | msc 30-00 |
Synonym | sequence of nth roots of n |