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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2 thoughts on “2011-13 Sums of Partial Sums

  1. Sukang

    수열 An이 m번째 항까지 모두 0이면, Tm=0이니깐
    Am/Tm이 정의되지 않는데, 이럴땐 Am/Tm을 0으로 생각하면 되나요?

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