Harmonic series is an infinite series of the form \(\sum_{n=1}^{\infty} \frac{1}{n}\). Its name derives from the concept of harmonics (overtones) in music: the wavelengths of the overtones of a vibrating string are \(\frac{1}{2}\), \(\frac{1}{3}\), \(\frac{1}{4}\), etc., of the string’s length. The demo below shows how the partial sum \(S\) grows as \(n \to \infty\). Can you tell if it converges to a number?