Inegalitate non-standard cu patrate

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Filip Chindea
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Joined: Thu Sep 27, 2007 9:01 pm
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Inegalitate non-standard cu patrate

Post by Filip Chindea »

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 ]
Life is complex: it has real and imaginary components.
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