Factorial inequality

Show that $(n!)^3 < n^nigl( rac{n+1}{2} ight)^{2n}$ .

~20 minProof · checked by AIInequalitiesFactorialsArithmetic-Geometric Mean

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIX. Inequalities, Examples XIX.a, No. 20

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