USAMO 1994 Problem 4

$\mathrm{x}_{\mathrm{i}}$ is a infinite sequence of positive reals such that for all $\mathrm{n}, \mathrm{x}_{1}+\mathrm{x}_{2}+\ldots+\mathrm{x}_{\mathrm{n}} \geq \sqrt{ }$. Show that $\mathrm{x}_{1}{ }^{2}+\mathrm{x}_{2}{ }^{2}+\ldots+$ $\mathrm{x}_{\mathrm{n}}^{2}>(1+1 / 2+1 / 3+\ldots+1 / \mathrm{n}) / 4$ for all $\mathrm{n}$.