수학동아 - 폴리매스

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Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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Function: mkdir

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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함께 풀고 싶은 문제

창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.

[창의 퍼즐] 곱 삼각형, 합 직각이등변삼각형

Amath 2021.10.06 03:04 조회 426

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

곱 삼각형은 파스칼의 삼각형을 살짝 변형한 것이다. 곱 삼각형은 2에서 시작한다.

a b

형태로 수가 있을 때 c는 a와 b의 곱이다.

그래서,

2 2

2 4 2

2 8 8 2

2 16 64 16 2

.......

형태로 파스칼의 삼각형과 같은 형태로 나열된다고 곱 삼각형을 정의하자.

문제 1. 곱 삼각형의 n째 줄의 k번째 수를 시그마를 사용하지 않고 n과 k를 이용한 식으로 나타내어라.

n 합 직각이등변 삼각형은

1 2 3 4 ... n

3 5 7 ...

8 12 ...

형태로,

a b

형태에서 c는 a+b이다. 그래서 한 줄씩 내려갈수록 그 줄의 숫자는 하나씩 줄어든다.

문제 2-1. 각 줄의 숫자들을 왼쪽에서 오른쪽의 순서로 나열할 때, 이렇게 만들어진 수열은 항상 등비수열임을 보이시오.

문제 2-2. n 합 직각이등변삼각형의 m번째 줄의 k번째 숫자를 $A(m,k)$ 라 할 때, $A(m,1)$ 의 점화식을 구하시오.

문제 2-3. n 합 직각이등변삼각형의 m번째 줄의 k번째 숫자를 $A(m,k)$ 라 할 때, $A(m,1)$ 의 점화식을 이용하여 $A(m,1)$ 의 일반항을 구하시오.

문제 2-4. n 합 직각이등변삼각형의 $A(m,k)$ 의 일반항을 구하시오.

이전글 (스토리 문제) 알락할미새와 노랑할미새의 모험 4

다음글 이상한 나라의 이상한 감방 1

이 문제 어떠셨나요?

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Amath Lv.8 2021.10.06 03:06

문제 1과 문제 2-1~2-4는 다른 묶음이라고 생각하고, 한 묶음당 해결 하나입니다.

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부분해결

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켋 Lv.7 2021.10.09 01:28 비밀댓글

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- Amath Lv.8 2021.10.09 02:41 비밀댓글
  
  비밀 댓글이 등록 되었습니다!
- Amath Lv.8 2021.10.09 06:06
  
  실수로 해결을 줘야 하는데 부분해결을 눌렀습니다. 다시 '정답요청'이라고 써서 정답요청해주세요.
  
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- Amath Lv.8 2021.10.09 06:15 비밀댓글
  
  비밀 댓글이 등록 되었습니다!

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