I was trying to do this problem:
Let $a_n$ be a sequence such that $a_{i+1}\leq a_i+a_j$ for all $i,j\in\mathbb{N}$. Prove that $a_1+a_2/2+\cdots+a_n/n\geq a_n$ for all $n\in\mathbb{N}$.
I tried induction; base case is trivial but have no idea what to do next.
Any help is appreciated