Anh thanh

Tính $\lim_{n \to +\infty}\dfrac{\sqrt{n!}}{n}$

\[\mathop {\lim }\limits_{n \to + \infty } \frac{{\sqrt {n!} }}{n} = \mathop {\lim }\limits_{n \to + \infty } \frac{{\sqrt n .\sqrt {(n - 1)!} }}{n} = \mathop {\lim }\limits_{n \to + \infty } \frac{{\sqrt {(n - 1)} .\sqrt {(n - 2)!} }}{{\sqrt n }}\]
\[ = \mathop {\lim }\limits_{n \to + \infty } \sqrt {\frac{{n - 1}}{n}} .\sqrt {(n - 2)!} = \mathop {\lim }\limits_{n \to + \infty } \sqrt {1 - \frac{1}{n}} .\sqrt {(n - 2)!} = + \infty \]

ta co the lam nhu sau: