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Part of 1954 Miklós Schweitzer

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Miklós Schweitzer 1954- Problem 1

Source: Miklós Schweitzer 1954- Problem 1

8/3/2015
1. Given a positive integer r>1r>1, prove that there exists an infinite number of infinite geometrical series, with positive terms, having the sum 1 and satisfying the following condition: for any positive real numbers S1,S2,…,SrS_{1},S_{2},\dots,S_{r} such that S1+S2+⋯+Sr=1S_{1}+S_{2}+\dots+S_{r}=1, any of these infinite geometrical series can be divided into rr infinite series(not necessarily geometrical) having the sums S1,S2,…,SrS_{1},S_{2},\dots,S_{r}, respectively. (S. 6)
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