Show that $\sum ^\infty_{k=1} a_k$ is divergent

Question

Let $\{a_k\}$ be sequence of positive numbers and suppose that $$a_k \leq a_{2k+1}+a_{2k}, \forall \;k=0,1,2...$$

Then show that $\sum ^\infty_{k=1} a_k$ is divergent

I really have no idea where to start this question from using given condition...

Thank you....

Answer 1

Hint: $$\sum_{k=2^{n+1}}^{2^{n+2}-1} a_k \ge \sum_{k=2^n}^{2^{n+1}-1} a_k$$