About a Conjecture: $-\left(\frac{x^{n}+1}{x^{n-1}+1}\right)^{n}-\left(\frac{x+1}{2}\right)^{n}+\left(x^{\frac{x}{x+1}}+\sqrt{x}-1\right)^{n}+1\leq 0$

score 98 · Answer 14 · 2022-06-25 10:35:24

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Prove an inequality with Jensen's inequality and its companion

Published on 25 Jun 2022 - 10:35

score 111 · Answer 15 · 2022-07-24 12:00:01

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Proof verification for proof by Karamata

Published on 24 Jul 2022 - 12:00

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About a Conjecture: $-\left(\frac{x^{n}+1}{x^{n-1}+1}\right)^{n}-\left(\frac{x+1}{2}\right)^{n}+\left(x^{\frac{x}{x+1}}+\sqrt{x}-1\right)^{n}+1\leq 0$

Prove an inequality with Jensen's inequality and its companion

Proof verification for proof by Karamata

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