11.8

Part of 2007 All-Russian Olympiad Regional Round

Problems(1)

n positive numbers

Source: Russian 2007

Prove that \prod_{i\equal{}1}^{n}(1\plus{}x_{1}\plus{}x_{2}\plus{}...\plus{}x_{i})\geq\sqrt{(n\plus{}1)^{n\plus{}1}x_{1}x_{2}...x_{n}}\forall x_{1},...,x_{n}> 0.

inequalitiesinductioninequalities proposed