5/7×5/11+5/7×2/11-5/7×14/11
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5/7×5/11+5/7×2/11-5/7×14/11
= 5/7 x ( 5/11 + 2/11 - 14/11 )
= 5/7 x -7/11
= -35/77
b: \(27D=3^{14}+3^{17}+...+3^{2024}\)
\(\Leftrightarrow26D=3^{2024}-3^{11}\)
hay \(D=\dfrac{3^{2024}-3^{11}}{26}\)
c: \(25E=-5^4-5^6-...-5^{1002}\)
\(\Leftrightarrow24E=-5^{1002}+5^2\)
hay \(E=\dfrac{-5^{1002}+5^2}{24}\)
\(\frac{5}{7}.\frac{-5}{7}+\frac{5}{7}.\frac{-2}{11}-\frac{5}{7}.\frac{-14}{11}\)
\(=\frac{5}{7}.\left(\frac{-5}{7}+\frac{-2}{11}-\frac{-14}{11}\right)\)
\(=\frac{5}{7}.\frac{29}{77}\)
\(=\frac{145}{539}\)
\(\frac{5}{7}.\frac{12}{11}+\frac{9}{7}.\frac{2}{11}-\frac{5}{7}.\frac{14}{11}\)
\(=\frac{1}{7}.\frac{1}{11}.\left(5.12+9.2-5.14\right)\)
\(=\frac{1}{77}.\left(60+18-70\right)\)
\(=\frac{1}{77}.8=\frac{8}{77}\)
`5/7xx5/11+5/7xx2/11-5/7xx14/11`
`=5/7xx(5/11+2/11-14/11)`
`=5/7xx(-7/11)`
`=-5/11`
\(\dfrac{5}{7}\cdot\dfrac{6}{11}+\dfrac{5}{11}\cdot\dfrac{1}{7}-\dfrac{5}{7}\cdot\dfrac{14}{11}\)
\(=\dfrac{5}{7}\cdot\dfrac{6}{11}+\dfrac{5}{7}\cdot\dfrac{1}{11}-\dfrac{5}{7}\cdot\dfrac{14}{11}\)
\(=\dfrac{5}{7}\cdot\left(\dfrac{6}{11}+\dfrac{1}{11}-\dfrac{14}{11}\right)\)
\(=\dfrac{5}{7}\cdot\dfrac{-7}{11}=\dfrac{-5}{11}\)
\(\dfrac{5}{7}\cdot\dfrac{9}{11}+\dfrac{-5}{7}\cdot\dfrac{-2}{11}+\dfrac{1}{14}=\dfrac{45}{77}+\dfrac{10}{77}+\dfrac{1}{14}=\dfrac{5}{7}+\dfrac{1}{14}=\dfrac{10}{14}+\dfrac{1}{14}=\dfrac{11}{14}\)
\(\dfrac{5}{7}.\dfrac{9}{11}-\dfrac{5}{7}.-\dfrac{2}{11}+\dfrac{1}{14}=\dfrac{5}{7}.\left(\dfrac{9}{11}+\dfrac{2}{11}\right)+\dfrac{1}{14}=\dfrac{5}{7}.1+\dfrac{1}{14}=\dfrac{10+1}{14}=\dfrac{11}{14}\)
\(\dfrac{5}{7}\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)=\dfrac{5}{7}\times-\dfrac{7}{11}=\dfrac{-5}{11}\)
5/7 x ( 5/11 + 2/11 - 14/11) = 5/7 x -7/11 = -5/11