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#### Albert

##### Well-known member

- Jan 25, 2013

- 1,225

Given:

\(\displaystyle x>0,\, n\in\mathbb{N}\)

Prove:

\(\displaystyle (1+x)\times\left(1+x^2 \right)\times\left(1+x^3 \right)\times\cdots\times\left(1+x^n \right)\geq\left(1+x^{\large{\frac{n+1}{2}}} \right)^n\)

\(\displaystyle x>0,\, n\in\mathbb{N}\)

Prove:

\(\displaystyle (1+x)\times\left(1+x^2 \right)\times\left(1+x^3 \right)\times\cdots\times\left(1+x^n \right)\geq\left(1+x^{\large{\frac{n+1}{2}}} \right)^n\)

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