Inegalitate usoara
Posted: Sat Jul 11, 2009 10:02 pm
\( \left\{ \begin{array}{c}
a_{1},\ a_{2},\dots,\ a_{n}\in\left(0,\ +\infty\right)\\
S=\sum_{k=1}^{n}a_{k}\\
\ a_{n+1}=a_{1}\end{array}\right|\Longrightarrow\sum_{k=1}^{n}\sqrt{\frac{a_{k}+a_{k+1}}{2S-a_{k}-a_{k+1}}}\ge2 \)
Dumitru Acu
a_{1},\ a_{2},\dots,\ a_{n}\in\left(0,\ +\infty\right)\\
S=\sum_{k=1}^{n}a_{k}\\
\ a_{n+1}=a_{1}\end{array}\right|\Longrightarrow\sum_{k=1}^{n}\sqrt{\frac{a_{k}+a_{k+1}}{2S-a_{k}-a_{k+1}}}\ge2 \)
Dumitru Acu