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Harmonic Sequence Calculator

Generate a harmonic sequence (reciprocals of an arithmetic sequence), its nth term and partial sum.

Enter values

Results update as you type.

Result

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

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

  1. Enter first term of the arithmetic sequence, common difference, terms.
  2. The result updates instantly as you type — press Calculate (or Enter) at any time.
  3. Review the breakdown shown under the main result.
  4. 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