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.

Read more about this topic:  Harmonic Series (mathematics)

Famous quotes containing the words partial and/or sums:

    We were soon in the smooth water of the Quakish Lake,... and we had our first, but a partial view of Ktaadn, its summit veiled in clouds, like a dark isthmus in that quarter, connecting the heavens with the earth.
    Henry David Thoreau (1817–1862)

    At Timon’s villalet us pass a day,
    Where all cry out,What sums are thrown away!’
    Alexander Pope (1688–1744)