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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 \(E=\dfrac{-5^{1002}+5^2}{24}\)
\(\frac{5}{7}.\frac{-5}{7}+\frac{5}{7}.\frac{-2}{11}-\frac{5}{7}.\frac{-14}{11}\)
\(=\frac{5}{7}.\left(\frac{-5}{7}+\frac{-2}{11}-\frac{-14}{11}\right)\)
\(=\frac{5}{7}.\frac{29}{77}\)
\(=\frac{145}{539}\)
\(\dfrac{5}{7}\cdot\dfrac{9}{11}+\dfrac{-5}{7}\cdot\dfrac{-2}{11}+\dfrac{1}{14}=\dfrac{45}{77}+\dfrac{10}{77}+\dfrac{1}{14}=\dfrac{5}{7}+\dfrac{1}{14}=\dfrac{10}{14}+\dfrac{1}{14}=\dfrac{11}{14}\)
\(\dfrac{5}{7}.\dfrac{9}{11}-\dfrac{5}{7}.-\dfrac{2}{11}+\dfrac{1}{14}=\dfrac{5}{7}.\left(\dfrac{9}{11}+\dfrac{2}{11}\right)+\dfrac{1}{14}=\dfrac{5}{7}.1+\dfrac{1}{14}=\dfrac{10+1}{14}=\dfrac{11}{14}\)
a: =35/17-18/17-9/5+4/5
=1-1=0
b: =-7/19(3/17+8/11-1)
=7/19*18/187=126/3553
c: =26/15-11/15-17/3-6/13
=1-6/13-17/3
=7/13-17/3=-200/39
\(-\frac{12}{35}\div\frac{7}{11}-\frac{23}{35}\div\frac{7}{11}-\frac{5}{11}\)
\(=\left(-\frac{12}{35}-\frac{23}{35}\right)\div\frac{7}{11}-\frac{5}{11}\)
\(=-1\div\frac{7}{11}-\frac{5}{11}\)
\(=-\frac{11}{7}-\frac{5}{11}\)
\(=-\frac{156}{77}\)
B=4*13/9*3-4/3*40/9
B=4/3*13/9-4/3*40/9
B=4/3*(13/9-40/9)
B=4/3*(-27)/9
B=4*(-3)/9
B=-4
A=6/7 + 1/7.(2/7+5/7)
A=6/7 + 1/7.7/7=6/7+1/7.1
A=6/7+1/7=7/7=1
a: \(=\dfrac{5}{7}\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)=\dfrac{5}{7}\cdot\dfrac{-7}{11}=-\dfrac{5}{11}\)
b: \(=\dfrac{12}{7}\left(19+\dfrac{5}{8}-15-\dfrac{1}{4}\right)=\dfrac{12}{7}\cdot\left(4+\dfrac{3}{8}\right)\)
\(=\dfrac{12}{7}\cdot\dfrac{35}{8}=\dfrac{3}{2}\cdot5=\dfrac{15}{2}\)
c: \(=\dfrac{2}{15}-\dfrac{2}{15}\cdot5+\dfrac{3}{15}=\dfrac{2}{15}\cdot\left(-4\right)+\dfrac{3}{15}=\dfrac{-8+3}{15}=\dfrac{-5}{15}=-\dfrac{1}{3}\)
d: \(=\dfrac{4}{9}\left(19+\dfrac{1}{3}-39-\dfrac{1}{3}\right)=\dfrac{4}{9}\cdot\left(-20\right)=-\dfrac{80}{9}\)
\(a,-\dfrac{5}{9}+\dfrac{14}{9}=\dfrac{-5+14}{9}=\dfrac{9}{9}=1\\ b,\dfrac{2}{7}+\dfrac{8}{-3}\\ =\dfrac{2}{7}-\dfrac{8}{3}\\ =\dfrac{2.3-8.7}{21}\\ =\dfrac{6-56}{21}\\ =\dfrac{-50}{21}\\ c,\dfrac{9}{11}+\dfrac{5}{7}+\dfrac{20}{-11}+\dfrac{12}{25}+\dfrac{2}{7}\\ =\left(\dfrac{2}{7}+\dfrac{5}{7}\right)+\left(\dfrac{9}{11}-\dfrac{20}{11}\right)+\dfrac{12}{25}\\ =\dfrac{7}{7}-\dfrac{11}{11}+\dfrac{12}{25}\\ =1-1+\dfrac{12}{25}\\ =\dfrac{12}{25}\)
\(\dfrac{5}{7}\left(\dfrac{5}{11}+\dfrac{2}{11}-\dfrac{14}{11}\right)=\dfrac{5}{7}\times-\dfrac{7}{11}=\dfrac{-5}{11}\)
5/7 x ( 5/11 + 2/11 - 14/11) = 5/7 x -7/11 = -5/11