MathDB
another tanh inequality

Source: VJIMC 2014 1.3

May 20, 2021
inequalities

Problem Statement

Let n≥2n\ge2 be an integer and let x>0x>0 be a real number. Prove that (1−tanh⁡x)n+tanh⁡(nx)<1.\left(1-\sqrt{\tanh x}\right)^n+\sqrt{\tanh(nx)}<1.
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