APMO 2012/05

Discussion on Asian Pacific Mathematical Olympiad (APMO)
Post Reply
User avatar
Nadim Ul Abrar
Posts:244
Joined:Sat May 07, 2011 12:36 pm
Location:B.A.R.D , kotbari , Comilla
APMO 2012/05

Unread post by Nadim Ul Abrar » Sat May 19, 2012 12:48 am

Let n be an integer greater than or equal to 2 . Peove that if the real numbers $a_1,a_2,...,a_n$ satisfy \[ a_1^2+a_2^2+...+a_n^2=n\] , then
\[\sum_{1\leq i < j \leq n} \frac{1}{n-a_ia_j} \leq \frac{n}{2}\]
must hold .
$\frac{1}{0}$
Top
Post Reply

Return to “Asian Pacific Math Olympiad (APMO)”