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Tính A=(1/2-1).(1/3-1).(1/4-1)...(1/100-1)

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\(A=\left(\dfrac{1}{2}-1\right)\cdot\left(\dfrac{1}{3}-1\right)\cdot\left(\dfrac{1}{4}-1\right)\cdot...\cdot\left(\dfrac{1}{100}-1\right)\)

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  • \(A=\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)\left(\dfrac{1}{4}-1\right)...\left(\dfrac{1}{100}-1\right)\)

    \(=\left(\dfrac{-1}{2}\right).\left(\dfrac{-2}{3}\right).\left(\dfrac{-3}{4}\right)...\left(\dfrac{-99}{100}\right)\) ( 99 phân số )

    \(=\dfrac{\left(-1\right)\left(-2\right)\left(-3\right)...\left(-99\right)}{2.3.4...100}=\dfrac{-1}{100}\)

    Vậy \(A=\dfrac{-1}{100}\)

      bởi Nguyễn Phương 26/12/2018
    Like (0) Báo cáo sai phạm

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