What is the limit as n approaches infinity of (n!)^n ?

The limit as n approaches infinity of (n!)^n is infinity

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limit as n approaches infinity of (n!)^n

n \to \infty lim ((n!)^{n})

\infty

Solution steps

n \to \infty lim (n!^{n})

Apply exponent rules

= n \to \infty lim (e^{n l n (n!)})

Apply the Limit Chain Rule:

\infty

= \infty

\int (\frac{2 x + 7}{x ^{2} + 2 x + 5}) d x

\frac{3 x}{( x + 1 ) ^{2}} (0)

6 x + y^{^{''}} = 0

(x^{4} - sec (4 x^{2} - 2))^{- 4}

\frac{\partial}{\partial x} (\frac{y}{x ^{2}})

What is the limit as n approaches infinity of (n!)^n ?
The limit as n approaches infinity of (n!)^n is infinity