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

解

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

0

解答ステップ

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

不定形式の場合を除く

= \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}

無限大の特性を適用する:

\frac{c}{\infty} = 0

= 0