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A real sequence

Source: Iran National Olympiad (3rd Round) 2001

July 13, 2007
searchalgebra proposedalgebra

Problem Statement

Does there exist a sequence {bi}i=1∞ \{b_{i}\}_{i=1}^\infty of positive real numbers such that for each natural m m: bm+b2m+b3m+⋯=1m b_{m}+b_{2m}+b_{3m}+\dots=\frac1m
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