Question 26
Let $n$ be an integer and let $0\lt u_1\lt u_2\lt\cdots\lt u_n$ be real numbers such that
$$u_1+u_2+\cdots+u_n=\frac1{u_1^2}+\frac1{u_2^2}+\cdots+\frac1{u_n^2}.$$
Show that, for every integer $k$ less than or equal to $n$, there are $k$ of these real numbers whose sum is at least $k$.
$$u_1+u_2+\cdots+u_n=\frac1{u_1^2}+\frac1{u_2^2}+\cdots+\frac1{u_n^2}.$$
Show that, for every integer $k$ less than or equal to $n$, there are $k$ of these real numbers whose sum is at least $k$.