Harmonic Series (mathematics) - Partial Sums

Partial Sums

The nth partial sum of the diverging harmonic series,

is called the nth harmonic number.

The difference between the nth harmonic number and the natural logarithm of n converges to the Euler–Mascheroni constant.

The difference between distinct harmonic numbers is never an integer.

No harmonic numbers are integers, except for n = 1.

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