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Question Number 172439 by Physicien last updated on 27/Jun/22

Commented by mr W last updated on 27/Jun/22

$t h i s a p p E q u a t i o n E d i t o r i s m a d e f o r$ $w r i t i n g e q u a t i o n s . W h y {d o n}^{'} t y o u$ $u s e i t f o r w r i t i n g e q u a t i o n s / f o r m u l a s$ $i n s t e a d o f p o s t i n g p i c t u r e s ? i s i t$ $f o r y o u n o t e a s i e r a n d b e t t e r t o w r i t e$ $\lim_{x \to \infty} \frac{x!}{x^{x} e^{- x} \sqrt{x}} ? t o b e h o n e s t, t h e$ $h a n d w r i t i n g y o u r p i c t u r e s s h o w i s$ $n o t t h e b e s t .$
Commented by Rasheed.Sindhi last updated on 27/Jun/22

$B T W a t y p e d q u e s t i o n i s m u c h h e l p f u l$ $i n c o p y - p a s t e a l s o .$
	Answered by qaz last updated on 27/Jun/22

	$\underset{n \to \infty}{l i m} \frac{n!}{n^{n} e^{- n} \sqrt{n}} = \underset{n \to \infty}{l i m} \frac{\sqrt{2 π n} {(\frac{n}{e})}^{n}}{n^{n} e^{- n} \sqrt{n}} = \sqrt{2 π} [n! \sim \sqrt{2 π n} {(\frac{n}{e})}^{n}, n \to \infty]$
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