MathDB

Let

x_1 , \dots , x_{2024}

be non negative real numbers with

\displaystyle{\sum_{i=1}^{2024}}x_i = 1

. Find, with proof, the minimum and maximum possible values of the following expression

\sum_{i=1}^{1012} x_i + \sum_{i=1013}^{2024} x_i^2 .

P6