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[잡담] 라마누잔의 합
17수락 2021.01.09 08:10 조회 873
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페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

모든 자연수의 합이 -1/12 라는 것에서

어떤 오류가 있죠?

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  •  
    수학동아 Lv.8 2021.01.09 18:53

    라마누잔합 - 나무위키 (namu.wiki)에 따르면 이 식은 ∣x∣<1 에서 정의되므로, 원칙적으로 x=1에서는 정의되진 않는다. 좌극한은 존재하나 우극한이 존재하지 않기 때문이다. 하지만, 정의된다고 가정하면 그 값은 1/4이다.이 식이 1-2+3-4+5-6+7...인데 1+2+3+...은 저거의 -3배여서 -1/12가 나오는데 앞에서 x=1일때 정의되지 않는다고 하였으나 x=1일때 정의해 틀린 것입니다.

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    •  
      17수락 Lv.9 2021.01.09 20:34

      그러니까 정확히 말하면 틀린 것이지만 x=1일때를 가정을 안하므로 옳다고 볼 수도 있는 것이죠?

      좋아요0
    •  
      수학동아 Lv.8 2021.01.09 21:00

      @수락

      저도 정확히 이해는 못했지만 원래 x=1일때 안되는데 된다면 -1/12이란 것 같아요.

      좋아요0
  •  
    △π Lv.9 2021.01.10 02:02

    "0으로 나누기"

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