Harmonic series is the sum of the elements of harmonic series. As early as14th century, Nicole oris had proved the divergence of harmonic series, but few people knew it. Oresme, a mathematician in the late Middle Ages, proved that all harmonic series diverge from infinity. But the Ramanukin sum of harmonic series exists and is Euler constant.

Harmonic series is one of the oldest and most basic series in mathematics. Its name comes from the harmony interval in music, that is, the interval in which the frequency ratio of two notes is an integer ratio. The nature of harmonic series occupies an important position in the history of mathematics, which is closely related to the concepts of prime number, Euler constant and Riemann zeta function.