2015 is coming!

Algebra Level 3

If \(\frac { { a }_{ 1 } }{ { a }_{ 2 }+{ a }_{ 3 }+...+{ a }_{ 2015 } } +\frac { { a }_{ 2 } }{ { a }_{ 1 }+{ a }_{ 3 }+...+{ a }_{ 2015 } } +\frac { { a }_{ 3 } }{ { a }_{ 1 }+{ a }_{ 2 }+{ a }_{ 4 }+...+{ a }_{ 2015 } } +...+\frac { { a }_{ 2014 } }{ { a }_{ 1 }+{ a }_{ 2 }+...+{ a }_{ 2013 }+{ a }_{ 2015 } } +\frac { { a }_{ 2015 } }{ { a }_{ 1 }+{ a }_{ 2 }+...+{ a }_{ 2014 } } \ge K\) find \(K\)

Details and assumptions:

  • \({ a }_{ 1 },{ a }_{ 2 },...,{ a }_{ 2014 },{ a }_{ 2015 }\) are positive real numbers.

  • Give your answer to 4 decimals


This problem was inspired by \(Nesbitt.......no\) by Kristian Vasilev

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