What is the limit as n approaches infinity of 1/(n!) ?

The limit as n approaches infinity of 1/(n!) is 0

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limit as n approaches infinity of 1/(n!)

n \to \infty lim (\frac{1}{n !})

0

Solution steps

n \to \infty lim (\frac{1}{n !})

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

= \frac{lim _{n \to \infty} ( 1 )}{lim _{n \to \infty} ( n ! )}

n \to \infty lim (1) = 1

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

= \frac{1}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

x \to 0 lim (\frac{1}{x ^{2} ( x + 8 )})

y^{^{''}} + 4 y = sin (2 x)

\int_{0}^{8} 3 x d x

\frac{d y}{d x} + 4 y^{2} = 0

\int \frac{1}{t t ^{2} - 1} d t

What is the limit as n approaches infinity of 1/(n!) ?
The limit as n approaches infinity of 1/(n!) is 0