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Function: driver
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수학동아 - 폴리매스
함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
mwryan
2020.05.05 08:27
조회 666
"모든 항이 자연수이고 공차가 1 이상인 임의의 등차수열에서, 모든 항을 역수 취해서 합한 값은 1/1=1을 제외하고는 절대 정수가 될 수 없다."라는 명제를 증명 또는 반증하여라.
(제 친구가 이 문제를 반년 넘게 계속 고민하고 있는데 모르겠다네요. 문제가 간단하길래 저도 같이 고민해봤는데... 어렵더라고요ㅠ 댓글에다 같이 토론하면서 풀어봅시다)
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모든 소수의 역수의 합은 발산한다는 정리가 있더라고요, 공차가 1이나 2일때 등등의 증명은 쉽게 되는데 모든 자연수 공차에 대해 성립할지는 모르겠네요.
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아인수타인
Lv.12
2020.05.05 08:31
어 저도 지금 1년하고 1개월 동안 친구와 같이 연구 중인 문제가 있는데...
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아인수타인
Lv.12
2020.05.05 11:51
좋아요0
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아인수타인
Lv.12
2020.05.05 11:53
좋아요0
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△π
Lv.9
2020.05.05 15:57
그게...
조화급수의 합 공식 구하기는 수학계에서 아직 안 풀린 난제중 하나입니다...
만약 이거 푸시면 필즈상각...(아닐수도?)
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△π
Lv.9
2020.05.05 16:00
근삿값을 구하기 위해서는 1/x까지 더했을 때 ln(x+1)이라고 하네요. 오차 0.6 미만으로 구한 값이라네요...
좋아요0
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