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27 tháng 1 2022
\(A=\dfrac{1}{5}\left(\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+...+\dfrac{1}{496}-\dfrac{1}{501}\right)\)
\(=\dfrac{1}{5}\cdot\dfrac{55}{334}=\dfrac{11}{334}\)
\(B=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{19}-\dfrac{1}{21}=\dfrac{20}{21}\)
23 tháng 6 2022
b: \(\Leftrightarrow1-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{34}+...+\dfrac{1}{89}-\dfrac{1}{100}+x=\dfrac{5}{3}\)
=>x+99/100=5/3
=>x=5/3-99/100=203/300
c: \(\Leftrightarrow\left(\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{15}+...+\dfrac{1}{19}-\dfrac{1}{21}\right)-x+4+\dfrac{221}{231}=\dfrac{7}{3}\)
\(\Leftrightarrow\dfrac{10}{231}-x+4+\dfrac{221}{231}=\dfrac{7}{3}\)
=>5-x=7/3
hay x=8/3
24 tháng 8 2021
c: Ta có: 11+x:5=13
\(\Leftrightarrow x:5=2\)
hay x=10
d: Ta có: \(13+2\left(x+1\right)=15\)
\(\Leftrightarrow2x+2=2\)
\(\Leftrightarrow2x=0\)
hay x=0
e: Ta có: 2x+21=41
\(\Leftrightarrow2x=20\)
hay x=10
f: Ta có: \(12+3\left(x-2\right)=60\)
\(\Leftrightarrow3\left(x-2\right)=48\)
\(\Leftrightarrow x-2=16\)
hay x=18
24 tháng 8 2021
g: Ta có: \(24x-11\cdot13=11\cdot11\)
\(\Leftrightarrow24x=11\cdot24\)
hay x=11
h: Ta có: \(17-\left(x-4\right):2=3\)
\(\Leftrightarrow\left(x-4\right):2=14\)
\(\Leftrightarrow x-4=28\)
hay x=32
6 tháng 8 2023
Tính:
\(\dfrac{10}{21}-1\cdot251+\dfrac{11}{21}+2\cdot251\\ 251\cdot\left(\dfrac{10}{21}+\dfrac{11}{21}\right)+\left(2-1\right)\\ 251\cdot1+1=252\)
Tìm x
c,\(\left(3x-1\right)^2:7=7\\ \left(3x-1\right)^2=7\cdot7=14\\ \left(3x-1\right)^2=\left(\pm7\right)^2\\ \Rightarrow\left[{}\begin{matrix}3x-1=7\\3x-1=-7\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}3x=7+1=8\\3x=-7+1=-6\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{8}{3}\\x=-\dfrac{6}{3}=-2\end{matrix}\right.\)
Vậy x={8/3;-2}
d; \(\left(7-2x\right)^3=\left(\dfrac{1}{2}\right)^2\cdot\left(-\dfrac{1}{2}\right)\\ \left(7-2x\right)^3=\left(-\dfrac{1}{2}\right)^3\\ 7-2x=-\dfrac{1}{2}\\ 2x=7--\dfrac{1}{2}=\dfrac{15}{2}\\ x=\dfrac{15}{2}:2=\dfrac{15}{4}\)
Z
0
BK
1
DP
25 tháng 7 2017
\(\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+....+\frac{2}{x\left(x+1\right)}=\frac{11}{40}\)
\(\Leftrightarrow\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+....+\frac{2}{x\left(x+1\right)}=\frac{11}{40}\)
\(\Leftrightarrow\frac{2}{5.6}+\frac{2}{6.7}+\frac{2}{7.8}+....+\frac{2}{x\left(x+1\right)}=\frac{11}{40}\)
\(\Leftrightarrow2\left(\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+....+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{11}{40}\)
\(\Leftrightarrow\frac{1}{5}-\frac{1}{x+1}=\frac{11}{40}\div2\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{5}-\frac{11}{80}\)
\(\Leftrightarrow\frac{1}{x+1}=\frac{1}{16}\Rightarrow x=16-1=15\)
LN
1
C
27 tháng 2 2023
\(\dfrac{11}{8}:x-\dfrac{2}{5}+-\dfrac{1}{6}=-\dfrac{1}{5}\\ =>\dfrac{11}{8}:x-\dfrac{2}{5}=-\dfrac{1}{5}-\left(-\dfrac{1}{6}\right)\\ =>\dfrac{11}{8}:x-\dfrac{2}{5}=-\dfrac{1}{5}+\dfrac{1}{6}\\ =>\dfrac{11}{8}:x-\dfrac{2}{5}=-\dfrac{6}{30}+\dfrac{5}{30}\\ =>\dfrac{11}{8}:x-\dfrac{2}{5}=-\dfrac{1}{30}\\ =>\dfrac{11}{8}:x=-\dfrac{1}{30}+\dfrac{2}{5}\\ =>\dfrac{11}{8}:x=-\dfrac{1}{30}+\dfrac{12}{30}\\ =>\dfrac{11}{8}:x=\dfrac{11}{30}\\ =>x=\dfrac{11}{8}:\dfrac{11}{30}\\ =>x=\dfrac{11}{8}.\dfrac{30}{11}\\ =>x=\dfrac{30}{8}\\ =>x=\dfrac{15}{4}\\ \dfrac{4}{7}x-\dfrac{1}{3}x+\left(-\dfrac{16}{21}\right)=-\dfrac{2}{3}\\ =>\left(\dfrac{4}{7}-\dfrac{1}{3}\right)x=-\dfrac{2}{3}-\left(-\dfrac{16}{21}\right)\\ =>\left(\dfrac{12}{21}-\dfrac{7}{21}\right)x=-\dfrac{2}{3}+\dfrac{16}{21}\\ =>\dfrac{5}{21}x=-\dfrac{14}{21}+\dfrac{16}{21}\\ =>\dfrac{5}{21}x=\dfrac{2}{21}\\ =>x=\dfrac{2}{21}:\dfrac{5}{21}\)
\(=>x=\dfrac{2}{21}.\dfrac{21}{5}\\ =>x=\dfrac{2}{5}\\ -\dfrac{11}{12}x+\dfrac{15}{2}\left(x+-\dfrac{1}{5}\right)=\dfrac{67}{8}\\ =>-\dfrac{11}{12}x+\dfrac{15}{2}.x-\dfrac{1}{5}=\dfrac{67}{8}\\ =>\left(-\dfrac{11}{12}+\dfrac{15}{2}\right)x=\dfrac{67}{8}+\dfrac{1}{5}\\ =>\left(-\dfrac{11}{12}+\dfrac{90}{12}\right)x=\dfrac{335}{40}+\dfrac{8}{40}\\ =>\dfrac{79}{12}x=\dfrac{343}{40}\\ =>x=\dfrac{343}{40}:\dfrac{79}{12}\\ =>x=\dfrac{343}{40}.\dfrac{12}{79}\\ =>x=\dfrac{343.12}{40.79}\\ =>x=\dfrac{343.3}{10.79}\\ =>x=\dfrac{1029}{790}\)
\(2\left(x-1\right)+11=21\Rightarrow2\left(x-1\right)=10\Rightarrow x-1=5\)
\(\Rightarrow x=6\)
2 ( x - 1 ) + 11 = 21
2x - 2 + 11 = 21
2x + 9 = 21
2x + 21 + 9
2 . x = 30
x = 30 : 2
x = 15