# 2011-13 Sums of Partial Sums

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.)

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