Harmonic Number and Series Calculator is a free online tool for calculating the sum of harmonic numbers and the Nth harmonic number.
What is a harmonic series and number?
A harmonic series is an infinite series, which is the sum of a special harmonic sequence. The formula for the harmonic series is
The first n terms of a harmonic series are called the Nth harmonic number.
First 100 harmonic numbers
- 1
- 1.5
- 1.833333
- 2.083333
- 2.283333
- 2.45
- 2.592857
- 2.717857
- 2.828968
- 2.928968
- 3.019877
- 3.103211
- 3.180134
- 3.251562
- 3.318229
- 3.380729
- 3.439553
- 3.495108
- 3.54774
- 3.59774
- 3.645359
- 3.690813
- 3.734292
- 3.775958
- 3.815958
- 3.85442
- 3.891457
- 3.927171
- 3.961654
- 3.994987
- 4.027245
- 4.058495
- 4.088798
- 4.11821
- 4.146781
- 4.174559
- 4.201586
- 4.227902
- 4.253543
- 4.278543
- 4.302933
- 4.326743
- 4.349999
- 4.372726
- 4.394948
- 4.416687
- 4.437964
- 4.458797
- 4.479205
- 4.499205
- 4.518813
- 4.538044
- 4.556912
- 4.57543
- 4.593612
- 4.611469
- 4.629013
- 4.646255
- 4.663204
- 4.67987
- 4.696264
- 4.712393
- 4.728266
- 4.743891
- 4.759276
- 4.774427
- 4.789352
- 4.804058
- 4.818551
- 4.832837
- 4.846921
- 4.86081
- 4.874509
- 4.888022
- 4.901356
- 4.914514
- 4.927501
- 4.940321
- 4.952979
- 4.965479
- 4.977825
- 4.99002
- 5.002068
- 5.013973
- 5.025738
- 5.037366
- 5.04886
- 5.060224
- 5.071459
- 5.082571
- 5.09356
- 5.104429
- 5.115182
- 5.12582
- 5.136346
- 5.146763
- 5.157072
- 5.167277
- 5.177378
- 5.187378
How to use the harmonic number and series Calculator
Using the calculator is very simple, enter the number of items into the input box and click Calculate button to get the answer.
For example, what are the 5th harmonic number and the sum of the first 5 harmonic numbers?
Enter 5 in the input box and click calculate button.
As shown in the figure, the 5th harmonic number is 13760. The sum of the first 5 harmonic numbers is 8.7.
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