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(1-1/10)x(1-1/11)x(1-1/12)x(1-1x1/13)=\(\dfrac{9}{10}\)x\(\dfrac{10}{11}\)x\(\dfrac{11}{12}\)x\(\dfrac{12}{13}\)=\(\dfrac{9}{13}\).
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Ta có \(\frac{1}{2004}.\left(1-\frac{1}{2005}\right).\left(1-\frac{1}{2006}\right).\left(1-\frac{1}{2007}\right).\left(1-\frac{1}{2008}\right)\)
\(=\frac{1}{2004}.\frac{2004}{2005}.\frac{2005}{.2006}.\frac{2006}{2007}.\frac{2007}{2008}\)
\(=\frac{1.2004.2005.2006.2007}{2004.2005.2006.2007.2008}\)
\(=\frac{1}{2008}\)
\(\frac{1}{2004}\cdot\left(1-\frac{1}{2005}\right)\cdot\left(1-\frac{1}{2006}\right)\cdot\left(1-\frac{1}{2007}\right)\cdot\left(1-\frac{1}{2008}\right)\)
\(=\frac{1}{2004}\cdot\frac{2004}{2005}\cdot\frac{2005}{2006}\cdot\frac{2006}{2007}\cdot\frac{2007}{2008}\)
\(=\frac{1\cdot2004\cdot2005\cdot2006\cdot2007}{2004\cdot2005\cdot2006\cdot2007\cdot2008}=\frac{1}{2008}\)
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cái thứ nhất là 2015,cái thứ hai là 403 đúng đây mình làm trong violympic được 100 điểm
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\(1\frac{1}{5}x1\frac{1}{6}x....x1\frac{1}{2014}=\frac{6}{5}x\frac{7}{6}x...x\frac{2015}{2014}=\frac{6x7x...x2015}{5x6x...2014}=\frac{2015}{5}=403\)
vậy x=403
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