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수학동아 - 폴리매스
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함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
[창의 퍼즐] 연속수열
유한의끝도못본남자 2019.11.15 03:01 조회 486

수열이는 어떤이상한 수열을 발견했다

그수열에는 연속수열이라고 적혀있었다

1,22,222,3333,333333,3333333,44444444...

규칙을 찾았는가?

그렇다. 숫자 n이 n번반복되면서 k항번반복해 연속되는 수열이다

연속수열의집합 N을가정하자

\sum_{k = 0}^{10000}N{_{k}}^{}(단, N{_{K}}^{}는 집합N의 k번째항이다)

를구하라

이 문제 어떠셨나요?

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