"조화급수와 조화 평균에서 '조화'란?"의 두 판 사이의 차이
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| 1번째 줄: | 1번째 줄: | ||
* <math>1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n}+\cdots</math> | * <math>1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n}+\cdots</math> | ||
| − | * (몰라도 되는 | + | * (몰라도 되는 식 하나) <math>\lim_{n \to \infty}\Big((1+\frac{1}{2}+\cdots+\frac{1}{n}) - \ln n \Big)</math> : 수렴한다. (수렴값 = 0.5772…) ([http://en.wikipedia.org/wiki/Euler-Mascheroni_constant 링크] 참조)<br> 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.<br> |
2009년 5월 13일 (수) 04:08 판
- \(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n}+\cdots\)
- (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.
- What's Harmonic about the Harmonic Series?
- David E. Kullman
- The College Mathematics Journal, Vol. 32, No. 3 (May, 2001), pp. 201-203