Prove, using Jensen's formula if $f(x) = x^\alpha, (\alpha > 1)$ is convex.$$\left(\sum_{i=1}^n x_i \right)^\alpha \leq n^{\alpha-1} \left(\sum_{i=1}^n x_i^\alpha \right)$$
Any tips on how to get this done? I can't really see much of a connection between Jensen's inequality and this one. It may be silly, but I'm really stuck here.