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

Toán Lớp 7: 1/2014 -1/2014.2013 -1/2013.2012=.1/3.2-1/2.1

Toán Lớp 7: 1/2014 -1/2014.2013 -1/2013.2012………….1/3.2-1/2.1

Comments ( 2 )

  1. 1/2014 – 1/{2014-2013} – …- 1/{3.2} – 1/{2.1}
    = 1/2014 – (1/{2014.2013} + …+ 1/{3.2} + 1/{2.1})
    = 1/2014 – (1/{1.2} + 1/{2.3} +…+ 1/{2013.2014})
    = 1/2014 – (1 – 1/2 + 1/2 – 1/3 +…+ 1/2013 – 1/2014)
    = 1/2014 – (1 – 1/2014)
    = 1/2014 – 1 + 1/2014
    = (1/2014 + 1/2014) – 1
    = 1/1007 – 1007/1007
    = -1006/1007

  2. 1/2014  – 1/( 2014 . 2013) – 1/( 2013 . 2012) – … – 1/( 3 . 2) – 1/( 2 . 1)
    = 1/2014 – (1/( 2014 . 2013) +  1/( 2013 . 2012) + … +1/( 3 . 2)  +1/( 2 . 1))
     = 1/2014 – ( 1/( 1 . 2) + 1/( 2 . 3) + … + 1/( 2012 . 2013) + 1/( 2013 . 2014))
    = 1/2014 – ( 1 – 1/2 + 1/2 – 1/3 + …+ 1/2012 – 1/2013 + 1/2013 – 1/2014)
    = 1/2014 – ( 1 – 1/2014)
    = 1/2014 – 2013/2014
    =-1006/1007
    #caty09

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