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Prove that a(1^(m))+a(2^(m))+…+a(n^(m))/...

Prove that `a_(1^(m))+a_(2^(m))+…+a_(n^(m))/(n)gt((a_(1)+a_(2)+…+a_(n))/(n))`,if m`lt`0 orm`gt`1 and `a_(i)gt0 forall`

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Let y =`f(x)=x^(m),where x gt 0 and 0 lt mlt1`
`(d^(2)y)/(dx^(2))=m(m-1)x^(m-2lt0`
So graph is concave downward
Therefore `(a_(1)^(m)+a_(2)^(m)+…a_(n)^(m))/(n)lt(a_(1)+a_(2)+…a_(n))/(n)^(n)`
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