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Sums of consecutive reciprocals
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The sum of the reciprocals of consecutive integers is never an integer. That is, for all positive integers m and n with n ≥ m, the sum is never an integer. This was proved by József Kürschák in 1908. This means that the harmonic numbers defined by are never integers. The harmonic series diverges, so […] The post Sums of consecutive reciprocals first appeared on John D. Cook.
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