IMO Shortlist 2001 problem A3
Dodao/la:
arhiva2. travnja 2012. Let
![x_1,x_2,\ldots,x_n](/media/m/3/a/4/3a498672e3108eccaf28c3c29f3916e2.png)
be arbitrary real numbers. Prove the inequality
%V0
Let $x_1,x_2,\ldots,x_n$ be arbitrary real numbers. Prove the inequality
$$\frac{x_1}{1+x_1^2} + \frac{x_2}{1+x_1^2 + x_2^2} + \cdots + \frac{x_n}{1 + x_1^2 + \cdots + x_n^2} < \sqrt{n}.$$
Izvor: Međunarodna matematička olimpijada, shortlist 2001