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Analysis 1. (Arithmetic mean ≥ geometric mean) x1 , x2 , · · · , xn > 0 , α1 , α2 , · · · , αn > 0, α1 + α2 + · · · + αn = 1. Show that α1 x1 + α2 x2 + · · · + αn xn ≥ xα1 1 xα2 2 · · · xαn
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Document Date: 2007-11-05 20:14:26
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Analysis 1. (Arithmetic mean ≥ geometric mean) x1 , x2 , · · · , xn > 0 , α1 , α2 , · · · , αn > 0, α1 + α2 + · · · + αn = 1. Show that α1 x1 + α2 x2 + · · · + αn xn ≥ xα1 1 xα2 2 · · · xαn