Generalization of Cauchy Inequality

Algebra Level 4

$\large\ \frac { { a }^{ 2017 } }{ b+c } +\frac { { b }^{ 2017 } }{ c+a } +\frac { { c }^{ 2017 } }{ a+b } \ge \frac { { a }^{ k }+{ b }^{ k }+{ c }^{ k } }{ 2 }$

If this inequality is satisfied for one value of $$k$$, find $$k$$.

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