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Function: driver
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Function: require_once
수학동아 - 폴리매스
Scubed
2021.01.12 02:43
조회 666
여러분들은 모든 자연수의 합이 발산한다는 생각이 맞다고 생각하십니까
리만제타함수의 -1의 값이 -1/12라고 모든 자연수의 합이 -1/12라는 주장이 맞다고 생각하십니까
저는 얘기를 들어보면 둘 다 맞는 것 같든데--;;
아 그리고 급수가지고 개소리하는(ex 1-1+1-1+...=1/2)건 또 어떻게 생각하시는지
p.s. 폴리매스 신입입니다
-
17수락
Lv.9
2021.01.12 03:34
어떻게 보면 이해가 되는데 또 저렇게 보면 말이 달라지죠.....
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전자기역학
Lv.8
2021.01.12 03:57
애초에 말이 달라질 것도 없습니다
1+1-1+1-1...도 결국 진동하기 때문에 발산하는 급수이고, 그거를 실수라고 가정하는 것부터 오류입니다
@수락
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라마누잔합은 결론부터말하자면
수적으론 틀렸습니다
무한한것을 상수로 취급했기 때문에
애초에 전건부정의오류입니다
1+x+x^2+...인 무한등비급수에
-x를 대입하면
1-x+x^2-x^3+x^4-...
무한등비급수공식에서 1/1+x인데
그리고 무등비식을 미분하면
-1+2x-3x^2+4x^3-...=- 1/(1+x)^2
양변에 -1을곱하면
1-2x+3x^2+...=1/(1+x)^2
x에 1의 좌극한을정의하면
1을대입할수있다
따라서 1-2+3-4+... =- 1/4
이며
양변의 -1을곱하면
2-1+4-3+5-4+...=1/4입니다
ㄷ
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자몽이
Lv.6
2021.01.12 05:20
지금 바로
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