"조화급수와 조화 평균에서 '조화'란?"의 두 판 사이의 차이
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(피타고라스님이 이 페이지의 이름을 조화급수와 조화 평균에서 '조화'란?로 바꾸었습니다.) |
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− | * <math>1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n}+\cdots</math> | + | <h5>간단한 소개</h5> |
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+ | * [[조화평균]] 항목 참조 | ||
+ | * | ||
+ | * 조화급수<br><math>1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{n}+\cdots</math><br> | ||
+ | * | ||
* (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> | * (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> | ||
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+ | <br> | ||
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+ | <h5>상위 주제</h5> | ||
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+ | ==== 하위페이지 ==== | ||
+ | |||
+ | * [[1964250|0 토픽용템플릿]]<br> | ||
+ | ** [[2060652|0 상위주제템플릿]]<br> | ||
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+ | <h5>재미있는 사실</h5> | ||
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+ | <h5>많이 나오는 질문과 답변</h5> | ||
+ | |||
+ | * 네이버 지식인<br> | ||
+ | ** http://kin.search.naver.com/search.naver?where=kin_qna&query= | ||
+ | ** http://kin.search.naver.com/search.naver?where=kin_qna&query= | ||
+ | ** http://kin.search.naver.com/search.naver?where=kin_qna&query= | ||
+ | ** http://kin.search.naver.com/search.naver?where=kin_qna&query= | ||
+ | ** http://kin.search.naver.com/search.naver?where=kin_qna&query= | ||
+ | |||
+ | |||
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+ | <h5>관련된 고교수학 또는 대학수학</h5> | ||
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+ | <h5>관련된 다른 주제들</h5> | ||
+ | |||
+ | * [[오일러상수, 감마]] | ||
+ | * [[수학사연표 (역사)|수학사연표]] | ||
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+ | <h5>관련도서 및 추천도서</h5> | ||
+ | |||
+ | * 도서내검색<br> | ||
+ | ** http://books.google.com/books?q= | ||
+ | ** http://book.daum.net/search/contentSearch.do?query= | ||
+ | * 도서검색<br> | ||
+ | ** http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords= | ||
+ | ** http://book.daum.net/search/mainSearch.do?query= | ||
+ | <h5>참고할만한 자료</h5> | ||
+ | |||
+ | * [http://en.wikipedia.org/wiki/Harmonic_series_%28mathematics%29 http://en.wikipedia.org/wiki/Harmonic_series_(mathematics)] | ||
+ | * http://en.wikipedia.org/wiki/Harmonic_mean | ||
* [http://www.jstor.org/stable/2687471 What's Harmonic about the Harmonic Series?]<br> | * [http://www.jstor.org/stable/2687471 What's Harmonic about the Harmonic Series?]<br> | ||
** David E. Kullman | ** David E. Kullman | ||
** <cite>The College Mathematics Journal</cite>, Vol. 32, No. 3 (May, 2001), pp. 201-203 | ** <cite>The College Mathematics Journal</cite>, Vol. 32, No. 3 (May, 2001), pp. 201-203 | ||
+ | * http://ko.wikipedia.org/wiki/ | ||
+ | * http://en.wikipedia.org/wiki/ | ||
+ | * http://viswiki.com/en/ | ||
+ | * http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q= | ||
+ | * http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7= | ||
+ | * 다음백과사전 http://enc.daum.net/dic100/search.do?q= | ||
+ | * [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집] | ||
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+ | <h5>관련기사</h5> | ||
+ | |||
+ | * 네이버 뉴스 검색 (키워드 수정)<br> | ||
+ | ** http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query= | ||
+ | ** http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query= | ||
+ | ** http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query= | ||
+ | ** http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query= | ||
+ | ** http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query= | ||
+ | |||
+ | |||
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+ | <h5>블로그</h5> | ||
+ | |||
+ | * 구글 블로그 검색 http://blogsearch.google.com/blogsearch?q= | ||
+ | * 트렌비 블로그 검색 http://www.trenb.com/search.qst?q= | ||
+ | |||
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+ | <h5>이미지 검색</h5> | ||
+ | |||
+ | * http://commons.wikimedia.org/w/index.php?title=Special%3ASearch&search= | ||
+ | * http://images.google.com/images?q= | ||
+ | * [http://www.artchive.com/ http://www.artchive.com] | ||
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+ | <h5>동영상</h5> | ||
+ | |||
+ | * http://www.youtube.com/results?search_type=&search_query= |
2009년 5월 13일 (수) 04:13 판
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.
상위 주제
하위페이지
재미있는 사실
많이 나오는 질문과 답변
- 네이버 지식인
- http://kin.search.naver.com/search.naver?where=kin_qna&query=
- http://kin.search.naver.com/search.naver?where=kin_qna&query=
- http://kin.search.naver.com/search.naver?where=kin_qna&query=
- http://kin.search.naver.com/search.naver?where=kin_qna&query=
- http://kin.search.naver.com/search.naver?where=kin_qna&query=
관련된 고교수학 또는 대학수학
관련된 다른 주제들
관련도서 및 추천도서
- 도서내검색
- 도서검색
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
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/
- http://viswiki.com/en/
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- 다음백과사전 http://enc.daum.net/dic100/search.do?q=
- 대한수학회 수학 학술 용어집
관련기사
- 네이버 뉴스 검색 (키워드 수정)
- http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
- http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
- http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
- http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
- http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=
블로그
- 구글 블로그 검색 http://blogsearch.google.com/blogsearch?q=
- 트렌비 블로그 검색 http://www.trenb.com/search.qst?q=
이미지 검색
- http://commons.wikimedia.org/w/index.php?title=Special%3ASearch&search=
- http://images.google.com/images?q=
- http://www.artchive.com