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Tìm x, biết 2/40+2/88+2/154+...+2/x(x+3)=202/1540

Tìm x biết \(\dfrac{2}{40}+\dfrac{2}{88}+\dfrac{2}{154}+.....+\dfrac{2}{x\left(x+3\right)}=\dfrac{202}{1540}\)

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  • \(\dfrac{2}{40}+\dfrac{2}{88}+...+\dfrac{2}{x\left(x+3\right)}=\dfrac{202}{1540}\)

    \(\Leftrightarrow2\left(\dfrac{1}{5\cdot8}+\dfrac{1}{8\cdot11}+...+\dfrac{1}{x\left(x+3\right)}\right)=\dfrac{202}{1540}\)

    \(\Leftrightarrow\dfrac{1}{5\cdot8}+\dfrac{1}{8\cdot11}+...+\dfrac{1}{x\left(x+3\right)}=\dfrac{101}{1540}\)

    \(\Leftrightarrow\dfrac{1}{3}\left(\dfrac{3}{5\cdot8}+\dfrac{3}{8\cdot11}+...+\dfrac{3}{x\left(x+3\right)}\right)=\dfrac{101}{1540}\)

    \(\Leftrightarrow\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{11}+...+\dfrac{1}{x}-\dfrac{1}{x+3}=\dfrac{303}{1540}\)

    \(\Leftrightarrow\dfrac{1}{5}-\dfrac{1}{x+3}=\dfrac{303}{1540}\)\(\Leftrightarrow\dfrac{1}{x+3}=\dfrac{1}{308}\)

    \(\Leftrightarrow x+3=308\Leftrightarrow x=305\)

      bởi Nguyen Thi Nhan 26/12/2018
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    Tìm x, biết:

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( với x thuộc Z)

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  • Cho A = 1+3+3\(^2\)+3\(^3\)+.....+3\(^{18}\)+3\(^{19}\)

    chung minh rang A chia het cho 4

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  • Bài 195 (Sách bài tập - tập 1 - trang 30)

    Một liên đội thiếu niên khi xếp hàng 2, hàng 3, hàng 4, hàng 5 đều thừa 1 người. Tính số đội viên của liên đội biết rằng số đó trong khoảng từ 100 đến 150 ?

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  • Bài 194 (Sách bài tập - tập 1 - trang 30)

    Cho biết \(m⋮n\). Tìm BCNN (m, n) ? Cho ví dụ ?

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  • Chứng minh \(\dfrac{12n+1}{30n+2}\) là phân số tối giản ( n thuộc N )

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  • Cho phép chia 49 : 7. Hãy tìm một số sao cho khi lấy số bị trừ trừ đi số đó, lấy số chia cộng với số đó thì được hai số mới mà thương của chúng bằng 1.

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  • Bài 193 (Sách bài tập - tập 1 - trang 30)

    Tìm các bội cung có ba chữ số của 63, 35, 105 ?

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