Let n 3 be an integer. For a permutation = (a₁, a₂, a_ n ) of (1,2, , n) we let f (x)=a_ n x^ n-1 +a^ n-1 + +a₂ x+a₁ . Let S be the sum of the roots of f (x)=0 and let S denote the sum over all permutation of (1,2, , n) of the number S_ . T

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Let n 3 be an integer. For a permutation = (a₁, a₂, a_ n ) of (1,2, , n) we let f (x)=a_ n x^ n-1 +a^ n-1 + +a₂ x+a₁ . Let S be the sum of the roots of f (x)=0 and let S denote the sum over all permutation of (1,2, , n) of the number S_ . Then

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Correct answer: A. S < -n !

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Let n 3 be an integer. For a permutation = (a₁, a₂, a_ n ) of (1,2, , n) we let f (x)=a_ n x^ n-1 +a^ n-1 + +a₂ x+a₁ . Let S be the sum of the roots of f (x)=0 and let S denote the sum over all permutation of (1,2, , n) of the number S_ . Then

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