An infinite number of terms...........with a finite value...........I think so anyways.......but with the exception of the fundamental........one...........all are 1/2.........and below......heading towards zero........................so how can u have infinity............in only half of a distance??  That implies that there are at least two infinities..........or does it?   B/c on the other side.........of 1/2, 1/3, 1/4, etc........u have 1/2, 2/3, 3/4, etc..................if u have the whole............................the other side filled or empty.........also has an infinite amount of terms............................

Harmonic series (mathematics)

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In mathematics, the harmonic series is the divergent infinite series:

${\displaystyle \sum _{n=1}^{\infty }{\frac {1}{n}}=1+{\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{4}}+{\frac {1}{5}}+\cdots }$

Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are 1/2, 1/3, 1/4, etc., of the string's fundamental wavelength. Every term of the series after the first is the harmonic mean of the neighboring terms; the phrase harmonic mean likewise derives from music.