## Help me out!!!

For students of class 9-10 (age 14-16)
sakibtanvir
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Joined: Mon Jan 09, 2012 6:52 pm
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### Help me out!!!

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.$i \in (1,2,3,....,n+1)$.
An amount of certain opposition is a great help to a man.Kites rise against,not with,the wind.

*Mahi*
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### Re: Help me out!!!

sakibtanvir wrote: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.$i \in (1,2,3,....,n+1)$.
The problem is from brilliant.org , for moral reasons, I request the other members of this forum to not post the solution/answer before next Monday.
Use $L^AT_EX$, It makes our work a lot easier!