Harmonic Number Calculator

Find the nth harmonic number.

Hₙ 2.929

Formula: Hₙ = 1 + 1/2 + 1/3 + … + 1/n

Step-by-step with your numbers:

1. Values used:

2. n = 10

4. Hₙ = 2.929

Did we solve your problem today?

The harmonic number sums the reciprocals of the first n integers.

The math behind it

Hₙ = Σ 1/k for k = 1..n. It grows slowly, roughly like ln(n) + 0.577.

H₁₀ ≈ 2.929.

Does it converge?

No — the harmonic series diverges to infinity, just very slowly.