2015 is coming!

Algebra Level 3

If a1a2+a3+...+a2015+a2a1+a3+...+a2015+a3a1+a2+a4+...+a2015+...+a2014a1+a2+...+a2013+a2015+a2015a1+a2+...+a2014K\frac { { a }_{ 1 } }{ { a }_{ 2 }+{ a }_{ 3 }+...+{ a }_{ 2015 } } +\frac { { a }_{ 2 } }{ { a }_{ 1 }+{ a }_{ 3 }+...+{ a }_{ 2015 } } +\frac { { a }_{ 3 } }{ { a }_{ 1 }+{ a }_{ 2 }+{ a }_{ 4 }+...+{ a }_{ 2015 } } +...+\frac { { a }_{ 2014 } }{ { a }_{ 1 }+{ a }_{ 2 }+...+{ a }_{ 2013 }+{ a }_{ 2015 } } +\frac { { a }_{ 2015 } }{ { a }_{ 1 }+{ a }_{ 2 }+...+{ a }_{ 2014 } } \ge K find KK

Details and assumptions:

  • a1,a2,...,a2014,a2015{ a }_{ 1 },{ a }_{ 2 },...,{ a }_{ 2014 },{ a }_{ 2015 } are positive real numbers.

  • Give your answer to 4 decimals


This problem was inspired by Nesbitt.......noNesbitt.......no by Kristian Vasilev

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