Let a₁, a₂, … be a sequence of non-negative real numbers less than or equal to 1. Let \(S_n=\sum_{i=1}^n a_i\) and \(T_n=\sum_{i=1}^n S_i\). Prove or disprove that \(\sum_{n=1}^\infty a_n/T_n\) converges. (Assume a₁>0.)

The best solution was submitted by Minjae Park (박민재), 2011학번. Congratulations!

Here is his Solution of Problem 2011-13. (There is a minor mistake in the proof.)

Alternative solutions were submitted by 어수강 (서울대학교 대학원, +2), 백진언 (한국과학영재학교, +2).