Inegalitate non-standard cu patrate
Posted: Sat Jul 12, 2008 6:40 pm
Fie realele nenegative \( a_1, ..., a_{100} \) cu suma patratelor \( 1 \), \( a_{101} := a_{101} \). Aratati ca
\( \sum_{k=1}^{100} a_k^2a_{k+1} < \frac{12}{25} \).
[ IMO Shortlist 2007, A6 ]
\( \sum_{k=1}^{100} a_k^2a_{k+1} < \frac{12}{25} \).
[ IMO Shortlist 2007, A6 ]