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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 7: (1+1/1.3).(1+1/2.4).(1+1/3.5)+…+(1+1/2014.2016)

Toán Lớp 7: (1+1/1.3).(1+1/2.4).(1+1/3.5)+…+(1+1/2014.2016)

Comments ( 2 )

  1. Lời giải và giải thích chi tiết:
    (1 + 1/(1 . 3))(1 + 1/(2 . 4))……(1 + 1/(2014 . 2016))
    = 4/(1 . 3) . 9/(2 . 4) . 16/(3 . 5) …….4060225/(2014 . 2016)
    = (2^2)/(1 . 3) . (3^2)/(2 . 4) ……….(2015^2)/(2014 . 2016)
    = (2^2 . 3^2 ……2015^2)/(1 . 3 . 2 . 4 . 3 . 5 ……….2014 . 2016)
    = (2 . 3 . 4 . 5 …….2015)/(1 . 2 . 3 ……..2014) . (2 . 3 . 4 ……2015)/(3 . 4 . 5 ….2016)
    = 2015 . 2/2016
    = 2015 . 1/1008
    = 2015/1008

  2. text{Giải đáp + Lời giải và giải thích chi tiết}
    (1+1/1.3).(1+1/2.4)…(1+1/2014.2016)
    =(1.3+1)/(1.3).(2.4+1)/(2.4)…(2014.2016+1)/(2014.2016)
    =(2.2)/(1.3).(3.3)/(2.4)…(2015.2015)/(2014.2016)
    =(2.2.3.3…2015.2015)/(1.3.2.4…2014.2016)
    =((2.3…2015).(2.3…2015))/((1.2…2014).(3.4…2016))
    =(2015.2)/(1.2016)
    =4030/2016
    2015/1008
    xin hay nhất.
     

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222-9+11+12:2*14+14 = ? ( )