What is the limit as n approaches infinity of (\sqrt[n]{n})/(ln(n)) ?

The limit as n approaches infinity of (\sqrt[n]{n})/(ln(n)) is 0

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limit as n approaches infinity of (\sqrt[n]{n})/(ln(n))

0

Solution steps

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

n \to \infty lim (ln (n)) = \infty

= \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

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What is the limit as n approaches infinity of (\sqrt[n]{n})/(ln(n)) ?
The limit as n approaches infinity of (\sqrt[n]{n})/(ln(n)) is 0