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Q1029 (Q1029): Difference between revisions - ArqMath20

Q1029 (Q1029): Difference between revisions

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Revision as of 12:30, 29 April 2020

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Statements

math-stackexchange-category

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B.8

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arqmath formula id

q_49

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math stackexcange post id

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relevant answers

Defining formula

\sqrt[n]{\frac{(27)^{n} (n!)^{3}}{(3 n)!}} \sim {(\frac{(27)^{n} {(\sqrt{2 π n} {(\frac{n}{e})}^{n})}^{3}}{\sqrt{6 π n} {(\frac{3 n}{e})}^{3 n}})}^{\frac{1}{n}} = \frac{27 {\sqrt{2 π}}^{\frac{3}{n}} n^{\frac{3}{2 n}} {(\frac{n}{e})}^{3}}{{\sqrt{6 π}}^{\frac{1}{n}} n^{\frac{1}{2 n}} {(\frac{3}{e})}^{3} n^{3}} = {(\frac{2 π n}{\sqrt{3}})}^{\frac{1}{n}}

lim_{n \to \infty} \sqrt[n]{\frac{(27)^{n} (n!)^{3}}{(3 n)!}} = 1

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