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d) \(B=\dfrac{1}{9.10}-\dfrac{1}{8.9}-...-\dfrac{1}{1.2}\)
\(=\dfrac{1}{9.10}-\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+...+\dfrac{1}{8.9}\right)\)
\(=\dfrac{1}{9.10}-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{8}-\dfrac{1}{9}\right)\)
\(=\dfrac{1}{9.10}-\left(1-\dfrac{1}{9}\right)\)
\(=\dfrac{1}{9.10}-\dfrac{8}{9}=-\dfrac{79}{90}\)
c: \(A=\left[\left(-\dfrac{3}{5}+\dfrac{4}{9}\right)\cdot\dfrac{7}{2}-\left(-\dfrac{14}{9}+\dfrac{2}{5}\right)\cdot\dfrac{7}{2}\right]:\left[\dfrac{23}{7}\left(7+\dfrac{1}{2}-5-\dfrac{1}{2}\right)\right]\)
\(=\dfrac{7}{2}\cdot\left(\dfrac{-3}{5}+\dfrac{4}{9}+\dfrac{14}{9}-\dfrac{2}{5}\right):\left[\dfrac{23}{7}\cdot2\right]\)
\(=\dfrac{7}{2}\cdot1:\dfrac{46}{7}=\dfrac{7}{2}\cdot\dfrac{7}{46}=\dfrac{49}{92}\)
d: \(B=\left(\dfrac{1}{9}-\dfrac{1}{10}\right)-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{8}-\dfrac{1}{9}\right)\)
=1/9-1/10-1+1/9
=2/9-1-1/10
=20/90-90/90-9/90=-79/90
c) \(A=\left[\left(-\dfrac{3}{5}+\dfrac{4}{9}\right):\dfrac{2}{7}-\left(-\dfrac{14}{9}+\dfrac{2}{5}\right):\dfrac{2}{7}\right]:\left(3\dfrac{2}{7}.7\dfrac{1}{2}-3\dfrac{2}{7}.5\dfrac{1}{2}\right)\)
\(\Rightarrow A=\left[\dfrac{7}{2}\left(-\dfrac{3}{5}+\dfrac{4}{9}+\dfrac{14}{9}-\dfrac{2}{5}\right)\right]:\left[\dfrac{23}{7}\left(7\dfrac{1}{2}-5\dfrac{1}{2}\right)\right]\)
\(\Rightarrow A=\left[\dfrac{7}{2}\left(2-1\right)\right]:\left(\dfrac{23}{7}.2\right)\)
\(\Rightarrow A=\dfrac{7}{2}:\dfrac{46}{7}=\dfrac{49}{92}\)
`c, A = [(-3/5 - 2/5 + 4/9 + 14/9) : 2/7] : (3 2/7 xx (7 1/2 - 5 1/2))`
`= 7 : 46/7`
`= 49/46`
`b, B = 1/10 - 1/9 + 1/9 - 1/8 + ... + 1/2 - 1/1`
`= 1/10 - 1/1 = -9/10`
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