( 1/1 nhân 2 + 1 /2 nhan3 + 1/3 nhân 4.........
Bài 4:
Ta có: \(\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{8\cdot9}+\dfrac{1}{9\cdot10}\right)\cdot100-\left[\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)\right]:\dfrac{1}{2}=89\)
\(\Leftrightarrow\left(1-\dfrac{1}{10}\right)\cdot100-\left[\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)\right]:\dfrac{1}{2}=89\)
\(\Leftrightarrow90-\left[\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)\right]:\dfrac{1}{2}=89\)
\(\Leftrightarrow\dfrac{5}{2}:\left(x+\dfrac{206}{102}\right):\dfrac{1}{2}=1\)
\(\Leftrightarrow\dfrac{5}{2}:\left(x+\dfrac{206}{102}\right)=2\)
\(\Leftrightarrow\left(x+\dfrac{206}{102}\right)=\dfrac{5}{4}\)
\(\Leftrightarrow x=\dfrac{-157}{204}\)
\(\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{9.10}\right).100-\left[\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)\right]:\dfrac{1}{2}=89\)
\(\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{9.10}\right).100-\left[\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)\right]=89.\dfrac{1}{2}\)
\(\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{9.10}\right).100-\left[\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)\right]=44,5\)
\(\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\right).100-\left[\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)\right]=44,5\)
\(\left(1-\dfrac{1}{10}\right).100-\left[\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)\right]=44,5\)
\(\dfrac{9}{10}.100-\left[\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)\right]=44,5\)
\(90-\left[\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)\right]=44,5\)
\(\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)=90-44,5\)
\(\dfrac{5}{2}:\left(x+\dfrac{206}{100}\right)=45,5\)
\(x+\dfrac{206}{100}=\dfrac{5}{2}:45,5\)
\(x+\dfrac{206}{100}=\dfrac{5}{91}\)
\(x=\dfrac{5}{91}-\dfrac{206}{100}=\dfrac{-9123}{4550}\)

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