# Math Help - How to solve this limit

1. ## How to solve this limit

How do you solve lim as n approaches infinity of (n^(1/n)+1)?

2. ## Re: How to solve this limit

Hint :

Set

$\ln A=\ln\left(n^{1/n}\right)$

and show :

$\lim_{n \to \infty}\ln A=0$

3. ## Re: How to solve this limit

lim n→∞ (n^(1/n)+1) = lim n→∞ (n^(1/n)) +1

lim n→∞ (n^(1/n)) is indeterminate, use L'Hopital's Rule
First change the limit into e^(lim n→∞ ln(n^(1/n))) = e^(lim n→∞ (1/n)*ln(n))
(1/n)*ln(n) = ∞/∞, take derivative of the numerator and the denominator
e^(lim n→∞ (1/n)) = 1

lim n→∞ (n^(1/n)+1) = 1+1 = 2