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

Toán Lớp 9: <3> Tính tổng a,P=4/1.2+4/2.3+4/3.4+…+4/99.100 b,S=1/x.(x+1)+1/(x+1).(x+2)+1/(x+2).(x+3)+…+ 1/(x+99).(x+100)

Toán Lớp 9: <3> Tính tổng
a,P=4/1.2+4/2.3+4/3.4+…+4/99.100
b,S=1/x.(x+1)+1/(x+1).(x+2)+1/(x+2).(x+3)+…+ 1/(x+99).(x+100)

Comments ( 2 )

  1.   P = 4/(1.2) + 4/(2.3) + …………… + 4/(99.100)
    1/4P = 1/(1.2) + 1/(2.3) + ……….. + 1/(99.100)
    1/4P = 1 – 1/2 + 1/2 – 1/3 + ……………… + 1/99 – 1/100
    1/4P = 99/100
    ⇒ P = 99/100 : 1/4 = 99/25
    S = 1/(x.(x+1)) + 1/((x + 1).(x + 2)) + …………… + 1/((x+99).(x+100)
    S = 1/x – 1/(x +1) + 1/(x + 1) – 1/(x + 2) + …………. + 1/(x + 99) – 1/(x + 100)
    S = 1/x – 1/(x + 100) 

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

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