About the Harmonic Sequence Calculator
Generate a harmonic sequence (reciprocals of an arithmetic sequence), its nth term and partial sum.
Also known as: harmonic progression, hp calculator, harmonic series.
How to use this calculator
- Enter first term of the arithmetic sequence, common difference, terms.
- The result updates instantly as you type — press Calculate (or Enter) at any time.
- Review the breakdown shown under the main result.
- Use Copy result or Share to save the answer or send a link with your inputs.
Formula
hₙ = 1 / (a₁ + (n − 1)d)
Worked example
Using the values pre-filled in the calculator above:
- First term of the arithmetic sequence = 1
- Common difference = 1
- Terms = 10
the calculator returns:
- Term 10: 0.1
- Partial sum: 2.92896825
- First terms: 1, 0.5, 0.3333, 0.25, 0.2, 0.1667, 0.1429, 0.125, 0.1111, 0.1