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Estonia — Open Contests

Algebra Difficulty 4.8 AIME Prove it Estonia

Publisher Soothsayer published a reference book claiming that for each real number $x$ and positive even number $n$ the equality $(1+x)^n \ge 2^n x$ holds. Is this claim true?

Solution

Answer: No.

The inequality does not hold for example when $x = \frac{1}{2}$ and $n = 4$ .

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.