BdMO Online Forum

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 \[a_{1}+\frac{a_{2}}{2}+...+\frac{a_{n}}{n}\geq a_{n},n\epsilon \mathbb{N}\].