Numere reale in intervalul [0,1]
Posted: Thu Feb 11, 2010 2:36 pm
Fie \( r_1,r_2,...,r_n \) numere reale in intervalul [0,1].Sa se arate ca exista o combinatie de \( \epsilon_k,1\leq k \leq n,\epsilon_k=-1,0,1 \) nu toate 0 astfel incat \( \left| {\sum\limits_{{\rm k = 1}}^{\rm n} {\varepsilon _k r_k } } \right| \le \frac{n}{{2^n }} \)