MathDB

A5

Part of 2014 Indonesia MO Shortlist

Problems(1)

(a_1+a_2+...+a_m)/m >= \sqrt{(a_1^2+a_2^2+...+a_{2014}^2)/2014} , max m

Source: INAMO Shortlist 2014 A5

5/21/2019
Determine the largest natural number mm such that for each non negative real numbers a1≥a2≥...≥a2014≥0a_1 \ge a_2 \ge ... \ge a_{2014} \ge 0 , it is true that a1+a2+...+amm≥a12+a22+...+a201422014\frac{a_1+a_2+...+a_m}{m}\ge \sqrt{\frac{a_1^2+a_2^2+...+a_{2014}^2}{2014}}
algebrainequalities