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

Toán Lớp 7: cho bài tập: D= 1/99 – 1/99.98 – 1/98.97–..-1/3.2 – 1/2.1

Toán Lớp 7: cho bài tập: D= 1/99 – 1/99.98 – 1/98.97……….-1/3.2 – 1/2.1

Comments ( 2 )

  1. 1/99 – 1/{99.98} – …- 1/{3.2} – 1/{2.1}
    = 1/99 – (1/{99.98} + …+ 1/{3.2} + 1/{2.1})
    = 1/99 – (1/{1.2} + 1/{2.3} +…+ 1/{98.99})
    = 1/99 – (1 – 1/2 + 1/2 – 1/3 +…+ 1/98 – 1/99)
    = 1/99 – (1 – 1/99)
    = 1/99 – 1 + 1/99
    = (1/99 + 1/99) – 1
    = 2/99 – 1
    = -97/99          
     

  2. D = 1/99 – 1/( 99 . 98) – 1/( 98 . 97) – … – 1/( 3 . 2) – 1/( 2 . 1)
    = 1/99 – (1/( 99 . 98) + 1/( 98 . 97) + … +1/( 3 . 2) +1/( 2 . 1))
    = 1/99 – (1/( 1 . 2) + 1/( 2 . 3) + … +  1/(97 . 98) + 1/( 98 . 99))
    = 1/99 – ( 1 – 1/2 + 1/2 – 1/3 + … + 1/97 – 1/98 + 1/98 – 1/99)
    = 1/99 – ( 1 – 1/99)
    = 1/99 – 1 + 1/99
    = ( 1/99 + 1/99) – 1
    = 2/99 – 1
    = 2/99 – 99/99
    =-97/99
    Vậy D =-97/99
    #caty09

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

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