MathDB

3#

Part of 2020 Junior Balkan Team Selection Tests-Serbia

Problems(1)

Inequality

Source: Serbia JBMO TST 2020 P3

9/5/2020
Given are real numbers a1,a2,...,a101a_1, a_2,...,a_{101} from the interval [−2,10][-2,10] such that their sum is 00. Prove that the sum of their squares is smaller than 20202020.
inequalities2020JBMO TST