Bounding Partial Sums of the Harmonic Series

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To get a lower bound on the partial sum of the harmonic series , replace the sum of the terms by for each , . This shows that the partial sum of the harmonic series is bounded below by . Move the slider to see the partial sums and this lower bound. Terms of the same color sum to

Contributed by: Matt Clay (March 2011)
Open content licensed under CC BY-NC-SA


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