MathDB
ln2*ln3*...ln n < sqrt(n!)/n

Source: VJIMC 2001 1.3

July 26, 2021
inequalities

Problem Statement

Let n≥2n\ge2 be a natural number. Prove that ∏k=2nln⁡k<n!n.\prod_{k=2}^n\ln k<\frac{\sqrt{n!}}n.
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