JBTST II 2010, Problema 2

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Andi Brojbeanu
Bernoulli
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Joined: Sun Mar 22, 2009 6:31 pm
Location: Targoviste (Dambovita)

JBTST II 2010, Problema 2

Post by Andi Brojbeanu »

Fie \( a_1, a_2, ..., a_n \) numere reale astfel incat
\( a_1+a_2+...a_n=0 \)
si
\( |a_1|+|a_2|+...+|a_n|=1 \).
Sa se arate ca:
\( |a_1+2a_2+...+na_n|\le\frac{n-1}{2} \).
Brojbeanu Andi Gabriel, clasa IX-a
Colegiul National "Constantin Carabella" Targoviste
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