Harmonic series math

In mathematics, the harmonic series is the divergent infinite series. Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are 12, 13, 14, etc., of the string's fundamental wavelength.

1. What is the harmonic series formula?
2. Why does the harmonic series diverge?
3. What is the order of the harmonic series?

What is the harmonic series formula?

The harmonic series is the sum from n = 1 to infinity with terms 1/n. If you write out the first few terms, the series unfolds as follows: 1 + 1/2 + 1/3 + 1/4 + 1/5 +. . .etc. As n tends to infinity, 1/n tends to 0.

Why does the harmonic series diverge?

Nth Term Test: The series diverge because the limit as goes to infinity is zero. Root Test: Since the limit as approaches to infinity is zero, the series is convergent.

What is the order of the harmonic series?

The harmonic series is an arithmetic progression (f, 2f, 3f, 4f, 5f, ...). In terms of frequency (measured in cycles per second, or hertz, where f is the fundamental frequency), the difference between consecutive harmonics is therefore constant and equal to the fundamental.