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

Toán Lớp 7: Tính A = 1/(3.5) + 1/(5.7) + … + 1/(97.99) B = -1/3 + 1/3^2 – 1/3^3 + … + 1/50 – 1/51

Tháng Sáu 21, 2022 Toán học 1 Comment 0 views

Toán Lớp 7: Tính
A = 1/(3.5) + 1/(5.7) + … + 1/(97.99)
B = -1/3 + 1/3^2 – 1/3^3 + … + 1/50 – 1/51

Comments ( 1 )

  1. quynhthanhnghi
    quynhthanhnghi
    21 Tháng Sáu, 2022 at 4:57 sáng
    Reply
    Giải đáp:
    A = 1/(3.5) + 1/(5.7) + … + 1/(97.99)
    => 2A = 2/(3.5) + 2/(5.7) + … + 2/(97.99)
    => 2A = {5 – 3}/{3.5} + {7 – 5}/{5.7} + … + {99 – 97}/{97.99}
    => 2A = 1/3 – 1/5 + 1/5 – 1/7 + … + 1/97 – 1/99
    => 2A = 1/3 + (-1/5 + 1/5) + … + (-1/97 + 1/97) – 1/99
    => 2A = 1/3 – 1/99
    => 2A = 32/99
    => A = 32/99 : 2
    => A = 16/99
    ———————————
    Sửa đề:
    B = -1/3 + 1/3^2 – 1/3^3 + … + 1/3^50 – 1/3^51
    => 3B = -1 + 1/3 – 1/3^2 + … + 1/3^49 – 1/3^50
    => 3B + B = (-1 + 1/3 – 1/3^2 + … + 1/3^49 – 1/3^50) + (-1/3 + 1/3^2 – 1/3^3 + … + 1/3^50 – 1/3^51)
    => 4B = -1 + 1/3 – 1/3^2 + … + 1/3^49 – 1/3^50  -1/3 + 1/3^2 – 1/3^3 + … + 1/3^50 – 1/3^51
    => 4B = -1 + (1/3 – 1/3) + (-1/3^2 + 1/3^2) + .. + (-1/3^50 + 1/3^50) – 1/3^51
    => 4B = -1 – 1/3^51
    => 4B = -{3^51 + 1}/3^51
    => B = -{3^51 + 1}/{4.3^51}

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

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