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FI-MO 1998 Problem 3

    Consider the geometric sequence 1/2, 1/4, 1/8,...1/2, \ 1 / 4, \ 1 / 8,... Can one choose a subsequence, finite or infinite, for which the ratio of consecutive terms is not 11 and whose sum is 1/5?1/5?

    Dataset text AI-MO AoPS. Quoted with source.

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