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Use our free harmonic series calculator to compute partial sums Hₙ = 1 + 1/2 + ... + 1/n, generalized harmonic series Σ1/i^k, and see the approximation ln(n)+γ.
The harmonic series is the sum of reciprocals of positive integers. It diverges slowly — Hₙ ~ ln(n) + γ (Euler-Mascheroni constant ≈ 0.5772). The generalized harmonic series Hₙ^(k) = Σ₁ⁿ 1/iᵏ converges when k > 1.
Hₙ = 1 + 1/2 + 1/3 + ... + 1/n ≈ ln(n) + γPercentage: The percentage value you want to apply
Number: The original number or value
Result: The calculated result
Result: 2.9289682540
Result: 1.5497677312
CalculateMe Team
Last updated: 2026-07-14