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lê minh đức

15/10/2017 at 18:04
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Tính nhanh.

\(\dfrac{1}{2}.\dfrac{1}{6}.......\dfrac{1}{110}\)


tính


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    Dao Trong Luan Coordinator 15/10/2017 at 18:31

    \(\dfrac{1}{2}\cdot\dfrac{1}{6}\cdot...\cdot\dfrac{1}{110}=\dfrac{1}{1\cdot2}\cdot\dfrac{1}{2\cdot3}\cdot...\cdot\dfrac{1}{10\cdot11}\)

    \(=\dfrac{1}{1\cdot2\cdot2\cdot3\cdot...\cdot10\cdot11}=\dfrac{1}{1\cdot2^2\cdot3^2\cdot...\cdot10^2\cdot11}\)

    \(=\dfrac{1}{4\cdot9\cdot16\cdot...\cdot100\cdot11}=\dfrac{1}{13168189440000\cdot11}=\dfrac{1}{144850083840000}\):V, I think the question is:

    \(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{110}\)

    \(=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{10\cdot11}=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{10}-\dfrac{1}{11}=1-\dfrac{1}{11}=\dfrac{10}{11}\)You should see again and write in English


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