Number Theory

    

Using the Partial Sums of the Alternating Harmonic Series to Prove the Harmonic Series is Divergent

Authors: Robert Spoljaric

Many proofs of the divergence of the harmonic series have been given since the first proof by Nicole Oresme (1323-1382). In this article we shall give a simple proof using the partial sums of the alternating harmonic series. A simple consequence of this is an approximation that follows as a corollary. We then show that every harmonic number is the sum of partial sums of the alternating harmonic series. Finally as a corollary we show that the sequence of subseries of the harmonic series is converging to ln2.

Comments: 5 Pages.

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Submission history

[v1] 2021-09-12 19:06:47
[v2] 2023-01-30 23:46:06
[v3] 2025-01-07 02:32:25

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