수학동아 - 폴리매스

함께 풀고 싶은 문제

창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.

[창의 퍼즐] [수열]피보나치 응용

전자기역학 2020.05.01 05:27 조회 660

문제 푼 사람 1명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

수열 $f_n$ 이 피보나치 수열이다(1, 1, 2, 3, 5, ...). 수열 $F_n$ 을 정의하기를,

$F_1=0, F_2=1$ 이며 양의 정수 n에 대해 $F_{n+2}=F_{n+1}+F_{n+1}F_n+F_n$ 을 만족하는 수열이다.

그럼 $n\geq 2$ 일 때, $F_n=2^{f_{n-1}}-1$ 임을 증명하여라.

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MathlabJ Lv.8 2020.05.01 18:07 비밀댓글

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- 전자기역학 Lv.8 2020.05.01 20:29 비밀댓글
  
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inf Lv.4 2020.05.02 01:46 비밀댓글

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- inf Lv.4 2020.05.02 01:47
  
  으악 TeX 가 깨지네요 나중에 이미지로 직접 렌더링해서 올리겠습니다
  
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