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anemone
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The real numbers $a,\,b,\,c,\,d$ are such that $a\ge b \ge c \ge d>0$ and $a+b+c+d=1$.
Prove that $(a+2b+3c+4d)a^ab^bc^cd^d<1$.
Prove that $(a+2b+3c+4d)a^ab^bc^cd^d<1$.