lê minh đức
15/10/2017 at 18:04-
\(\dfrac{1}{2}\cdot\dfrac{1}{6}\cdot...\cdot\dfrac{1}{110}=\dfrac{1}{1\cdot2}\cdot\dfrac{1}{2\cdot3}\cdot...\cdot\dfrac{1}{10\cdot11}\)
\(=\dfrac{1}{1\cdot2\cdot2\cdot3\cdot...\cdot10\cdot11}=\dfrac{1}{1\cdot2^2\cdot3^2\cdot...\cdot10^2\cdot11}\)
\(=\dfrac{1}{4\cdot9\cdot16\cdot...\cdot100\cdot11}=\dfrac{1}{13168189440000\cdot11}=\dfrac{1}{144850083840000}\):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