Shortlist 19

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Antonache Emanuel
Euclid
Posts: 37
Joined: Sat Feb 28, 2009 4:15 pm
Location: Targoviste, Dambovita

Shortlist 19

Post by Antonache Emanuel »

Demonstrati ca daca o functie \( f:{R}\rightarrow{R} \) are proprietatea:
\( |\sum_{k=1}^n 2^k(f(x+ky)-f(x-ky))|\le1 \), oricare \( n\in\mathbb{N}* \) si oricare \( x,y\in\mathbb{R} \), atunci f este constanta.
Farcas Csaba, Cluj, Shortlist 2007
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