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함께 풀고 싶은 문제

나도 수학쌤 문장제 문제를 변형해 문제를 내는 곳입니다.

[문장제 문제&개념응용] [수렴]수렴랜드

cho317jun 2021.04.28 04:22 조회 427

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

1. 옛날옛날 폴매타운에 수렴을 좋아하는 수렴이와 발산을 좋아하는 발산이가 살았다.

둘은 매우 친한 친구였다.

어느 날 수렴이가 발산이에게 말했다.

수렴: 발산아! 내가 오늘 땅바닥에서 수렴랜드 초청권을 받았어! 같이 가자.

발산: 난 발산이 더 좋은데... 그래도 뭐. 어쩔 수 없지. 인심 썼다!

수렴랜드에 도착한 수렴과 발산. 그들 앞에는 계단이 있었는데, 심상치 않은 계단이었다.

첫 번째 계단은 1층을, 두 번째 계단은 $\frac{1}{2}$ 층을, 세 번째 계단은 $\frac{1}{4}$ 층을... 이렇게 무한 개로 계단이 있었다.

수: 와! 이 계단식(?)은 2에 수렴하는구나!

안내자: 잘 아는구나. 그렇다면 한 번 증명해 볼래?

당신이 수렴이가 되어 위 수렴식이 2에 수렴함을 증명하시오.

2. 로비를 지나 세컨드로비로 갔더니 아까와 같은 계단인데 이번에는 첫 번째 계단은 1층을, 두 번째 계단은 $\frac{1}{3}$ 층을, 세 번째 계단은 $\frac{1}{9}$ 층을... 이렇게 무한 개로 계단이 있었다. 그렇다면 로비에 있던 수열과 세컨드로비에 있는 수열은 모두 2로 수렴하는가? 증명 또는 반증하시오.

다음 문제는 발산랜드로 이어집니다.

오류가 있다면 알림 주시고, 풀이 필수!

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△π Lv.9 2021.04.28 17:05 비밀댓글

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- cho317jun Lv.6 2021.04.29 06:55 비밀댓글
  
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△π Lv.9 2021.04.28 17:06 비밀댓글

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PF＿ Lv.8 2021.05.02 18:24 비밀댓글

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- cho317jun Lv.6 2021.05.07 03:01
  
  ...
  
  ~~(발산하는 매스티콘식) 크기가 25식 커집니다~~
  
  ~~(아닌가? 이거 나중에는 한도를 넘어 컴퓨터가 못 담을텐데...)~~
  
  좋아요0