Home Competitions KöMaL 2007 B3987
Let n ≥ n \ge n ≥ a 1 , a 2 , … , a n a_1,a_2,\ldots,a_n a 1 , a 2 , … , a n ( a 1 + a 2 + a 3 ) 2 ( a 2 + a 3 + a 4 ) 2 ⋅ … ⋅ ( a n − 1 + a n + a 1 ) 2 ( a n + a 1 + a 2 ) 2 {(a_1+a_2+a_3)}^2 {(a_2+a_3+a_4)}^2\cdot \ldots \cdot {(a_{n-1}+a_n+a_1)}^2{(a_n+a_1+a_2)}^2 ( a 1 + a 2 + a 3 ) 2 ( a 2 + a 3 + a 4 ) 2 ⋅ … ⋅ ( a n − 1 + a n + a 1 ) 2 ( a n + a 1 + a 2 ) 2 ≥ 2 n ( a 1 + a 2 ) 2 ( a 2 + a 3 ) 2 ⋅ … ⋅ ( a n − 1 + a n ) 2 ( a n + a 1 ) 2 . \ge 2^n{(a_1+a_2)}^2{(a_2+a_3)}^2\cdot \ldots \cdot {(a_{n-1}+a_n)}^2{(a_n+a_1)}^2. ≥ 2 n ( a 1 + a 2 ) 2 ( a 2 + a 3 ) 2 ⋅ … ⋅ ( a n − 1 + a n ) 2 ( a n + a 1 ) 2 .
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