What is the limit as n approaches infinity of (n!)^2 ?

The limit as n approaches infinity of (n!)^2 is infinity

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limit as n approaches infinity of (n!)^2

n \to \infty lim ((n!)^{2})

\infty

Solution steps

n \to \infty lim (n!^{2})

x \to a lim [f (x)]^{b} = [x \to a lim f (x)]^{b}

With the exception of indeterminate form

= (n \to \infty lim (n!))^{2}

Apply the common limit:

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

= \infty^{2}

Apply Infinity Property:

\infty^{c} = \infty

= \infty

What is the limit as n approaches infinity of (n!)^2 ?
The limit as n approaches infinity of (n!)^2 is infinity