Re: [中學] 分項對消法

看板Math作者mack (腦海裡依然記得妳)時間12年前 (2013/11/21 10:15)推噓3(3推 0噓 2→)

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※ 引述《t6370345 (貓咪QQ)》之銘言： : ___1_____ + ____1_____ = : 2*3*4*5 3*4*5*7 : 想請問這題限制使用分項消除的話該怎麼做呢? : 謝謝 1/(2*3*4*5) + 1/(3*4*5*6) = (1/3) * [1/(2*3*4) - 1/(3*4*5)] + (1/3) * [1/(3*4*5) - 1/(4*5*6)] = (1/3) * [1/(2*3*4) - 1/(4*5*6)] = (1/3) * (1/2) * {[1/(2*3) - 1/(3*4)] - [1/(4*5) - 1/(5*6)]} = (1/3) * (1/2) * [1/(2*3) - 1/(3*4) - 1/(4*5) + 1/(5*6)] = (1/3) * (1/2) * [(1/2 - 1/3) - (1/3 - 1/4) - (1/4 - 1/5) + (1/5 - 1/6)] = (1/3) * (1/2) * (1/2 - 2/3 + 2/5 - 1/6) = (1/3) * (1/2) * [(15-20+12-5)/30] = (1/3) * (1/2) * (2/30) = 1/90 1/(2*3*4*5) + 1/(3*4*5*6) = [1/(3*4*5)] * (1/2 + 1/6) = 1/(3*4*5) * (8/2*6) = 8/(2*3*4*5*6) = 1/(3*5*6) = 1/90 ...何樂不為 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 111.252.208.40

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mack

11/21 10:17, , 1^F

11/21 10:17, 1^F

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mack

11/21 10:18, , 2^F

11/21 10:18, 2^F

※ 編輯: mack 來自: 111.252.208.40 (11/21 10:20)

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t6370345

11/21 10:26, , 3^F