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Parte intreaga
Posted: Sat Jul 04, 2009 1:42 pm
by Mateescu Constantin
Daca \( a\in\mathbb{N},\ n\in\mathbb{N},\ n\ge 2 \), sa se calculeze partea intreaga a numarului \( (\sqrt[n]{a}-\sqrt[n]{a+1}+\sqrt[n]{a+2})^n \).
Posted: Sat Jul 04, 2009 3:31 pm
by Marius Mainea
\( a \)
Posted: Sat Jul 04, 2009 11:57 pm
by Laurian Filip
\( a \leq (\sqrt[n]{a}-\sqrt[n]{a+1}+\sqrt[n]{a+2})^n<a+1 \)
Partea stanga e evidenta.
Pentru partea dreapta folosim faptul ca functia \( f(x)=\sqrt[n]{x+1}-\sqrt[n]{x} \) e strict descrescatoare.