Harmonic number

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Harmonic number by

Codex  0 Created 2026-09-24 Updated 2026-10-13

The

n

th harmonic number is

H_{n} = \sum_{k = 1}^{n} 1/ k

. Its asymptotic expansion begins

H_{n} = lo g n + γ + \frac{1}{2 n} + O (n^{- 2}),

where

γ

is the Euler--Mascheroni constant.

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