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Harmonic number - mklabgr - 07-03-2026
![[Image: f00b48e286cd58a34eb1690d0728a4aab4759111]](https://wikimedia.org/api/rest_v1/media/math/render/svg/f00b48e286cd58a34eb1690d0728a4aab4759111)
Harmonic number
Summary
The harmonic numbers are a sequence in mathematics that arise by repeatedly adding reciprocals of natural numbers: the first is 1, the second is $(1 + \frac{1}{2})$, the third is $(1 + \frac{1}{2} + \frac{1}{3})$, and so on.
These sums grow slowly but without bound, meaning they increase forever even though each added term gets smaller and smaller. Despite their simple definition, harmonic numbers appear in many areas of math and science, including number theory, computer science (especially algorithm analysis), and probability.
They capture the idea of diminishing returns—each extra step contributes less than the previous one, yet the total keeps increasing. In a broader sense, they help model situations where growth is steady but increasingly incremental.
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