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 \(E=\dfrac{-5^{1002}+5^2}{24}\)

\(\frac{5}{7}.\frac{-5}{7}+\frac{5}{7}.\frac{-2}{11}-\frac{5}{7}.\frac{-14}{11}\)

\(=\frac{5}{7}.\left(\frac{-5}{7}+\frac{-2}{11}-\frac{-14}{11}\right)\)

\(=\frac{5}{7}.\frac{29}{77}\)

\(=\frac{145}{539}\)

\(\frac{5}{7}.\frac{12}{11}+\frac{9}{7}.\frac{2}{11}-\frac{5}{7}.\frac{14}{11}\)

\(=\frac{1}{7}.\frac{1}{11}.\left(5.12+9.2-5.14\right)\)

\(=\frac{1}{77}.\left(60+18-70\right)\)

\(=\frac{1}{77}.8=\frac{8}{77}\)

\(\frac{8}{77}\)nghe bn

`5/7xx5/11+5/7xx2/11-5/7xx14/11`

`=5/7xx(5/11+2/11-14/11)`

`=5/7xx(-7/11)`

`=-5/11`

\(\dfrac{5}{7}\times\dfrac{5}{11}+\dfrac{5}{7}\times\dfrac{2}{11}-\dfrac{5}{7}\times\dfrac{14}{11}\)

=\(\dfrac{5}{7}\times\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)\)

=\(\dfrac{5}{7}\)\(\times-\dfrac{7}{11}\)

=\(-\dfrac{5}{11}\)

Chúc bạn học tốt nhé

57×(511+211−1411)57×(511+211−1411)

=×−711×−711

=

\(\dfrac{5}{7}\cdot\dfrac{6}{11}+\dfrac{5}{11}\cdot\dfrac{1}{7}-\dfrac{5}{7}\cdot\dfrac{14}{11}\)

\(=\dfrac{5}{7}\cdot\dfrac{6}{11}+\dfrac{5}{7}\cdot\dfrac{1}{11}-\dfrac{5}{7}\cdot\dfrac{14}{11}\)

\(=\dfrac{5}{7}\cdot\left(\dfrac{6}{11}+\dfrac{1}{11}-\dfrac{14}{11}\right)\)

\(=\dfrac{5}{7}\cdot\dfrac{-7}{11}=\dfrac{-5}{11}\)

^{_{\(\dfrac{5}{7}\cdot\dfrac{9}{11}+\dfrac{-5}{7}\cdot\dfrac{-2}{11}+\dfrac{1}{14}=\dfrac{45}{77}+\dfrac{10}{77}+\dfrac{1}{14}=\dfrac{5}{7}+\dfrac{1}{14}=\dfrac{10}{14}+\dfrac{1}{14}=\dfrac{11}{14}\)}}

\(\dfrac{5}{7}.\dfrac{9}{11}-\dfrac{5}{7}.-\dfrac{2}{11}+\dfrac{1}{14}=\dfrac{5}{7}.\left(\dfrac{9}{11}+\dfrac{2}{11}\right)+\dfrac{1}{14}=\dfrac{5}{7}.1+\dfrac{1}{14}=\dfrac{10+1}{14}=\dfrac{11}{14}\)