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.
Read more about this topic: Harmonic Series (mathematics)
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—Henry David Thoreau (1817–1862)
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Where all cry out,What sums are thrown away!’”
—Alexander Pope (1688–1744)