Category Archives: harmonic numbers

The Divergence of the Harmonic Series

The fact that the harmonic series, , diverges has been known since the time of Nicole Oresme in the 14th century, but this fact is still somewhat surprising from a numerical standpoint.  After all, each successive term only adds a … Continue reading

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A Double Euler-Mascheroni Sequence

What is the value of the sum ?  Furdui poses this as Question 1.28 in his book Limits, Series, and Fractional Part Integrals [1, p. 5], where he calls the sum a “double Euler-Mascheroni sequence.”  His solution converts the double sum into an expression containing an integral … Continue reading

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