On a conjecture of Manickam and Singhi (Q1412669)

A short argument is given to show that if \((x_1,\dots,x_n)\) is a sequence of real numbers, \(\sum_{i} x_i\geq 0\), and \(n\geq 2^{k+1}e^k k^{k+1}\), then there are at least \({n-1 \choose k-1}\) \(k\)-element subsets \(I\) if the indices such that \(\sum_{i\in I} x_i \geq 0\).