Weighted Power Inequality

Show that $(\frac{a + b + c + \dots + k}{n})^{a + b + c + \dots + k} < a^{a} b^{b} c^{c} \dots k^{k}$ .

~15 minProof · checked by AIInequalitiesWeighted MeansLogarithmic Convexity

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XIX. Inequalities, Examples XIX.b, No. 6

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