APMO 1999-2

Discussion on Asian Pacific Mathematical Olympiad (APMO)
User avatar
SANZEED
Posts:550
Joined:Wed Dec 28, 2011 6:45 pm
Location:Mymensingh, Bangladesh
APMO 1999-2

Unread post by SANZEED » Sun Jun 03, 2012 2:23 am

Let $a_{1},a_{2},....$ be a sequence of real numbers satisfying $a_{i+j}\leq a_{i}+a_{j}$ for all $i,j=1,2,3,...$. Prove that \[a_{1}+\frac{a_{2}}{2}+...+\frac{a_{n}}{n}\geq a_{n},n\epsilon \mathbb{N}\].
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$

Post Reply