### Help me out!!!

Posted:

**Fri Feb 22, 2013 4:02 pm**Find the maximum value of the positive integer $n$ that satisfies the following inequality,

$a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+...+a_{n+1}^{2} \geq a_{n+1}(a_{1}+a_{2}+....+a_{n})$.

where $a_{i}$ is an arbitrary real number.$i \in (1,2,3,....,n+1)$.

$a_{1}^{2}+a_{2}^{2}+a_{3}^{2}+a_{4}^{2}+...+a_{n+1}^{2} \geq a_{n+1}(a_{1}+a_{2}+....+a_{n})$.

where $a_{i}$ is an arbitrary real number.$i \in (1,2,3,....,n+1)$.