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  • 1/3加1/5加1/7加1/9加1/11加1/33加1/35加1/45加1/55加1/77簡(jiǎn)算,

    1/3加1/5加1/7加1/9加1/11加1/33加1/35加1/45加1/55加1/77簡(jiǎn)算,
    數(shù)學(xué)人氣:321 ℃時(shí)間:2020-03-27 09:04:16
    優(yōu)質(zhì)解答
    1/3+1/5+1/7+1/9+1/11+1/33+1/35+1/45+1/55+1/77
    =1/3+1/5+1/7+1/9+1/11+(1/3-1/11)/8+(1/5-1/7)/2
    +(1/5-1/9)/4+(1/5-1/11)/6+(1/7-1/11)/4
    =1/3+1/5+1/7+1/9+1/11+(1/3)/8-(1/11)/8+(1/5)/2-(1/7)/2+
    (1/5)/4-(1/9)/4+(1/5)/6-(1/11)/6+(1/7)/4-(1/11)/4
    =(1/3)*[1+1/8]
    +(1/5)*[1+1/2+1/4+1/6]
    +(1/7)*[1-1/2+1/4]
    +(1/11)*[1-1/8-1/6-1/4]
    +(1/9)*[1-1/4]
    =(1/3)*(9/8)+(1/5)*(23/12)+(1/7)*(3/4)+(1/11)*(11/24)+(1/9)*(3/4)
    =(1/3)*(9/8)+(1/5)*(23/12)+(1/7)*(3/4)+1/24+1/12
    =(3/8)+(1/5)*(23/12)+(1/7)*(3/4)+1/8
    =1/2+(1/5)*(23/12)+(1/7)*(3/4)
    =(6*5*7+23*7+3*3*5)/(12*5*7)
    =[210+161+45]/(12*5*7)
    =416/(12*5*7)
    =104/105要寫這么多啊
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