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수학동아 - 폴리매스
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[수학 정보] 무한등비급수 쉽게 알아보기
khr519 2021.06.20 06:04 조회 533
공유하기
페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

1. 무한등비급수: 1+1/2+1/4+1/8........ 같이 무한히 긴 등비수열의 합.

2. 값 구하기: 위의 식을 보면 앞의 항의 1/2배씩 더해진다는 것을 알 수 있다.

즉 수열의 합을 A라고 하면 A=1+A*(1/2). 일차방정식 풀듯이 하면

A*(1-(1/2))=1

A=1/(1-(1/2))

즉 문자로 첫 항을 a, 공비를 r 이라고 하면 a/1-r

끝

 

추천 3 목록보기
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  •  
    Scubed Lv.7 2021.06.20 08:09

    + 수렴 구간 : -1초과 1미만일 때

    1이상 : 발산

    -1 이하 : 진동

    댓글 작성하기 좋아요1 댓글수1
    •  
      khr519 Lv.8 2021.06.20 19:11

      앗! 감사합니다! 

      좋아요0
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