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Part of 1951 Miklós Schweitzer

Problems(1)

Miklos Schweitzer 1951_1

Source:

Choose terms of the harmonic series so that the sum of the chosen terms be finite. Prove that the sequence of these terms is of density zero in the sequence

1,\frac12,\frac13,\dots,\frac1n,\dots

real analysisreal analysis unsolved