조화급수와 조화 평균에서 '조화'란?

간단한 소개

• 조화평균 항목 참조
•  
• 조화급수
  \(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n}+\cdots\)
  
•  
• (몰라도 되는 식 하나) \(\lim_{n \to \infty}\Big((1+\frac{1}{2}+\cdots+\frac{1}{n}) - \ln n \Big)\) : 수렴한다. (수렴값 = 0.5772…) (링크 참조)
  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 term harmonic mean likewise derives from music.
  

 

 

 

 

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참고할만한 자료

• http://en.wikipedia.org/wiki/Harmonic_series_(mathematics)
• http://en.wikipedia.org/wiki/Harmonic_mean
• What's Harmonic about the Harmonic Series?
  
  • David E. Kullman
  • The College Mathematics Journal, Vol. 32, No. 3 (May, 2001), pp. 201-203
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• http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
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