Problem A. 408. (October 2006)
A. 408. The positive reals and b1b2...bn satisfy a1+a2+...+akb1+b2+...+bk for all 1kn. Prove that
(5 pont)
Deadline expired on November 15, 2006.
Solution. Applying the weighted AM-HM inequality,
so
Estimate the last denominator as
Therefore,
Statistics:
14 students sent a solution. 5 points: Gyenizse Gergő, Hujter Bálint, Kisfaludi-Bak Sándor, Kónya 495 Gábor, Lovász László Miklós, Nagy 224 Csaba, Nagy 314 Dániel, Sümegi Károly, Tomon István, Wolosz János. 4 points: Korándi Dániel, Kornis Kristóf, Nagy 235 János. 3 points: 1 student.
Problems in Mathematics of KöMaL, October 2006