In mathematics, Maclaurin's inequality, named after Colin Maclaurin, is a refinement of the inequality of arithmetic and geometric means. Let a 1 , a 2 , … , a n {\displaystyle a_{1},a_{2},\ldots ,a_{n}} be non-negative real numbers, and for k = 1 , 2 , … , n {\displaystyle k=1,2,\ldots ,n} , define the averages S k {\displaystyle S_{k}} as follows: S k = ∑ 1 ≤ i 1 < ⋯ < i k ≤ n a i 1 a i 2 ⋯ a i k ( n k ) .
In mathematics, Maclaurin's inequality, named after Colin Maclaurin, is a refinement of the inequality of arithmetic and geometric means. Let a 1 , a 2 , … , a n {\displaystyle a_{1},a_{2},\ldots ,a_{n}} be non-negative real numbers, and for k = 1 , 2 , … , n {\displaystyle k=1,2,\ldots ,n} , define the averages S k {\displaystyle S_{k}} as follows: S k = ∑ 1 ≤ i 1 < ⋯ < i k ≤ n a i 1 a i 2 ⋯ a i k ( n k ) .
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