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

Toán Lớp 7: Cho `A=(1/4-1)(1/9-1)(1/16-1)…(1/10000-1).` So sánh A với `-1/2`

Toán Lớp 7: Cho A=(1/4-1)(1/9-1)(1/16-1)…(1/10000-1).
So sánh A với -1/2

Comments ( 1 )

  1. $\\$
    A=(1/4-1)(1/9-1)…(1/10000 – 1)
    = (-3)/4 . (-8)/9 … (-9999)/10000
    = – (3. 8…9999)/(4 . 9 … 100 00)
    = – (3 . 2 . 4 …. 99 . 101)/(2 . 2 . 3 . 3 … 100 . 100)
    = – (2 . 3 . 4 … 99)/(2 . 3 … 100) . (3 . 4 . 5 … 101)/(2 . 3 . 4 … 100)
    = – 1/100 . 101/2
    = (-101)/200 < (-100)/200 = (-1)/2
    =>A<(-1)/2
     

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