/sci/ - Science & Math

Let <span class="math">(a_n)[/spoiler] be a sequence of positive reals such that, for all <span class="math">n[/spoiler], <span class="math">a_n\leq a_{2n}+a_{2n+1}[/spoiler]. Prove that <span class="math">\sum_{n=1}^{\infty}a_n[/spoiler] diverges.