5^2/6×12+5^2/11×16+5^2/16×21+...+5^2/56×11
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TH
2
30 tháng 4 2019
52/1*6 + 52/6*11 + 52/11*16 + 52/16*21 + 52/21*26 + 52/26*31
=5(1-1/6+1/6-1/11+1/11-...+1/26-1/31)
=5(1-1/31)
=5.30/31
=150/31
30 tháng 4 2019
52/1 x 6 + 52/6 x 11 + 52/11 x 16 + 52/16 x 21 + 52/21 x 26 + 52/26 x 31
= 5.(5/1.6 + 5/6.11 + 5/11.16 + 5/16.21 + 5/21.26 + 5/26.31)
= 5.(1 - 1/6 + 1/6 - 1/11 + 1/11 - 1/16 + 1/16 - 1/21 + 1/21 - 1/26 + 1/26 - 1/31)
= 5.(1 - 1/31)
= 5.30/31
= 150/31
DD
1
9 tháng 10 2016
Bạn dùng công thức này mà làm nhé :\(\frac{n}{a\times\left(a+n\right)}=\frac{1}{a}-\frac{1}{a+n}\)
Ví dụ :\(\frac{2}{3\times5}=\frac{1}{3}-\frac{1}{5};\frac{3}{4\times7}=\frac{1}{4}-\frac{1}{7};\frac{5}{6\times11}=\frac{1}{6}-\frac{1}{11}\)
16 tháng 1 2022
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 \(E=\dfrac{-5^{1002}+5^2}{24}\)
H9
HT.Phong (9A5)
CTVHS
3 tháng 4 2023
\(\left(\dfrac{6:\dfrac{3}{5}-\dfrac{17}{16}.\dfrac{6}{7}}{\dfrac{21}{5}.\dfrac{10}{11}+\dfrac{57}{11}}-\dfrac{\left(\dfrac{3}{20}+\dfrac{1}{2}-\dfrac{1}{15}\right).\dfrac{12}{49}}{\dfrac{10}{3}+\dfrac{2}{9}}\right).x=\dfrac{215}{96}\)
\(\Rightarrow\left(\dfrac{\dfrac{509}{56}}{9}-\dfrac{\dfrac{7}{12}.\dfrac{12}{49}}{\dfrac{32}{9}}\right).x=\dfrac{215}{96}\)
\(\Rightarrow\left(\dfrac{509}{504}-\dfrac{\dfrac{1}{7}}{\dfrac{32}{9}}\right).x=\dfrac{215}{96}\)
\(\Rightarrow\left(\dfrac{509}{504}-\dfrac{9}{224}\right).x=\dfrac{215}{96}\)
\(\Rightarrow\dfrac{1955}{2016}.x=\dfrac{215}{96}\)
\(\Rightarrow x=\dfrac{215}{96}:\dfrac{1955}{2016}\)
\(\Rightarrow x=\dfrac{903}{391}\)
H
3 tháng 4 2023
`[ 6 : 3/5 - 17/16 . 6/7 : 21/5 . 10/11 + 57/11 - (3/20 + 1/2 - 1/15) . 12/49 : 10/3 + 2/9 ] . x = 215/96`
`=>[ 6 . 5/3 - 17/16 . 6/7 . 5/21 . 10/11 + 57/11 - (3/20 + 1/2 - 1/15) . 12/49 . 3/10 + 2/9 ] . x = 215/96`
`=>[10- 51/56 . 6/7 . 5/21 . 10/11 + 57/11 - (3/20 + 1/2 - 1/15) . 12/49 . 3/10 + 2/9 ] . x = 215/96`
`=> [10- 153/196 . 5/21 . 10/11 + 57/11 - (3/20 + 1/2 - 1/15) . 12/49 . 3/10 + 2/9 ] . x = 215/96`
`=> [10- 255/1372 . 10/11 + 57/11 - (3/20 + 1/2 - 1/15) . 12/49 . 3/10 + 2/9 ] . x = 215/96`
`=> [10- 1275/7546 + 57/11 - (3/20 + 1/2 - 1/15) . 12/49 . 3/10 + 2/9 ] . x = 215/96`
`=> (10- 1275/7546 + 57/11 - 7/12. 12/49 . 3/10 + 2/9 ) . x = 215/96`
`=> ( 10- 1275/7546 + 57/11 -343/600 . 3/10 + 2/9 ) . x = 215/96`
`=> ( 10- 1275/7546 + 57/11 -343/2000 + 2/9 ) . x = 215/96`
`=>15,06357671 . x= 215/96`
`=> x= 215/96: 15,06357671`
`=>x= 0,1486754027`
Đề có phải như vậy không nhỉ ?
LN
1
C
27 tháng 2 2023
\(\dfrac{11}{8}:x-\dfrac{2}{5}+-\dfrac{1}{6}=-\dfrac{1}{5}\\ =>\dfrac{11}{8}:x-\dfrac{2}{5}=-\dfrac{1}{5}-\left(-\dfrac{1}{6}\right)\\ =>\dfrac{11}{8}:x-\dfrac{2}{5}=-\dfrac{1}{5}+\dfrac{1}{6}\\ =>\dfrac{11}{8}:x-\dfrac{2}{5}=-\dfrac{6}{30}+\dfrac{5}{30}\\ =>\dfrac{11}{8}:x-\dfrac{2}{5}=-\dfrac{1}{30}\\ =>\dfrac{11}{8}:x=-\dfrac{1}{30}+\dfrac{2}{5}\\ =>\dfrac{11}{8}:x=-\dfrac{1}{30}+\dfrac{12}{30}\\ =>\dfrac{11}{8}:x=\dfrac{11}{30}\\ =>x=\dfrac{11}{8}:\dfrac{11}{30}\\ =>x=\dfrac{11}{8}.\dfrac{30}{11}\\ =>x=\dfrac{30}{8}\\ =>x=\dfrac{15}{4}\\ \dfrac{4}{7}x-\dfrac{1}{3}x+\left(-\dfrac{16}{21}\right)=-\dfrac{2}{3}\\ =>\left(\dfrac{4}{7}-\dfrac{1}{3}\right)x=-\dfrac{2}{3}-\left(-\dfrac{16}{21}\right)\\ =>\left(\dfrac{12}{21}-\dfrac{7}{21}\right)x=-\dfrac{2}{3}+\dfrac{16}{21}\\ =>\dfrac{5}{21}x=-\dfrac{14}{21}+\dfrac{16}{21}\\ =>\dfrac{5}{21}x=\dfrac{2}{21}\\ =>x=\dfrac{2}{21}:\dfrac{5}{21}\)
\(=>x=\dfrac{2}{21}.\dfrac{21}{5}\\ =>x=\dfrac{2}{5}\\ -\dfrac{11}{12}x+\dfrac{15}{2}\left(x+-\dfrac{1}{5}\right)=\dfrac{67}{8}\\ =>-\dfrac{11}{12}x+\dfrac{15}{2}.x-\dfrac{1}{5}=\dfrac{67}{8}\\ =>\left(-\dfrac{11}{12}+\dfrac{15}{2}\right)x=\dfrac{67}{8}+\dfrac{1}{5}\\ =>\left(-\dfrac{11}{12}+\dfrac{90}{12}\right)x=\dfrac{335}{40}+\dfrac{8}{40}\\ =>\dfrac{79}{12}x=\dfrac{343}{40}\\ =>x=\dfrac{343}{40}:\dfrac{79}{12}\\ =>x=\dfrac{343}{40}.\dfrac{12}{79}\\ =>x=\dfrac{343.12}{40.79}\\ =>x=\dfrac{343.3}{10.79}\\ =>x=\dfrac{1029}{790}\)
so easy
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