Show that if \(a, b, c\) are the lengths of the sides of a triangle and if \(2S=a+b+c,\) then \(\frac{a^n}{b+c}+\frac{b^n}{c+a}+\frac{c^n}{a+b} \geq (\frac{2}{3})^{n-2}S^{n-1} \forall n \in \mathbb{N}\)
