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Function: mkdir

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

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 585
Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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Function: getLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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Function: parseLatexImg

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
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Function: require_once

수학동아 - 폴리매스
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[잡담] 도움이 필요해요
Scubed 2021.08.08 19:50 조회 270

불쌍한 Scubed를 구해주세요

방법은 간단합니다. 자연수 a에 대해서

\int_{0}^{\frac{\pi }{2}}\cos 2ax\sin^{2a}xdx=(-1)^{a}\frac{\pi}{2^{2a+1}}

이라는 것과

\int_{0}^{\frac{\pi }{2}}\cos 2ax\sin^{2a+1}xdx=(-1)^{a}\frac{2^{2a}-1}{2^{4a-2}-(-1)^{a}}

를 증명해주세요

문제 아니고 저도 몰라요

그냥 계산기로 노가다하다 보니 나온 거에요

  •  
    Scubed Lv.7 2021.08.08 19:51

    참고로 저는 부분적분 이용해서 점화식 세워서 풀려고 했는데 실패했습니다. 여러분들은 저보다 똑똑하니 성공하실 수도...?

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