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Problem of the Week 1247

Harmonic Rational Enumeration

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Can the rational numbers in the interval [0, 1] be enumerated as a sequence q(1), q(2), ..., q(n), ... so that ∑q(n)/n as n goes from 1 to infinity converges?

Source: University of Michigan Undergraduate Mathematics Competition 17 (2000).

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18 August 2017