Calculate the n-th harmonic number Hn.
Last updated: June 2026 | By Patchworkr Team
The harmonic numbers add reciprocal terms from 1 through n.
Hn grows slowly and is well approximated by ln(n) + gamma + 1/(2n).
Calculate H5.
1. Add 1 + 1/2 + 1/3 + 1/4 + 1/5
2. Total = 2.283333...
Final answer: 2.28333333
Does Hn grow quickly?
No. It grows very slowly, roughly like a logarithm.
What is gamma?
It is the Euler-Mascheroni constant used in the approximation.
Can n be huge?
Yes, the approximation becomes very useful for large n.
Does the harmonic series converge?
No, the infinite series diverges.
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