Please help Show that lim_(n→∞) ((((3n)!)/((n!)^3 )))^(1/n) = 27


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Question Number 124537 by nimnim last updated on 04/Dec/20

$P l e a s e h e l p$ $S h o w t h a t \underset{n \to \infty}{l i m} {(\frac{(3 n)!}{{(n!)}^{3}})}^{1 / n} = 27$
	Answered by Dwaipayan Shikari last updated on 04/Dec/20

	$\lim_{x \to \infty} {(\frac{3^{3 n} n^{3 n} e^{- n} \sqrt{2 π n}}{n^{3 n} e^{- n} \sqrt{2 π n}})}^{\frac{1}{n}} = 27$
	Commented by mnjuly1970 last updated on 04/Dec/20

	$g o o d v e r y g o o d$ $s t i r l i n g a p p r o x i m a t i o n . . .$
	Commented by mohammad17 last updated on 05/Dec/20

	$h o w t h i s ?$
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