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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
(2/11.13+2/13.15+...+2/19.21)-x+4+221/231=7/3
(1/11-1/13+1/13-1/15+...+1/19-1/21)-x+4+221/231=7/3
(1/11-1/21)-x+4+221/231 =7/3
(21/231-11/231)-x+4+221/231 =7/3
10/231-x+4+221/231 =7/3
(10/231+221/231)-x+4 =7/3
231/231-x+4 =7/3
1-x+4 =7/3
-x+5 =7/3
-x =7/3-5
-x =7/3-15/3
-x =-8/3
x =8/3
ĐẶt A = 2/11.13 + 2/13.15 +...+2/19.21
A = 1/11 - 1/13 +1/ 13 -1/15 +....+1/19 - 1/21
A = 1/11 - 1/21
A = 10/231
Thay vào ta có
10/231 - x + 4 + 221 /231 = 7/3
-x + 4 + 1 = 7/3 ( vì 10/231 + 221/231 = 1)
-x + 5 = 7/3
-x = 7/3 - 5
-x = -8/3
x = 8/3
a.
\(\left(\frac{11}{12}+\frac{11}{12\times23}+\frac{11}{23\times34}+...+\frac{11}{89\times100}\right)+x=\frac{2}{3}\)
\(\left(\frac{11}{12}+\frac{1}{12}-\frac{1}{23}+\frac{1}{23}-\frac{1}{34}+...+\frac{1}{89}-\frac{1}{100}\right)+x=\frac{2}{3}\)
\(\left(\frac{11}{12}+\frac{1}{12}-\frac{1}{100}\right)+x=\frac{2}{3}\)
\(\left(\frac{12}{12}-\frac{1}{100}\right)+x=\frac{2}{3}\)
\(\left(1-\frac{1}{100}\right)+x=\frac{2}{3}\)
\(\left(\frac{100-1}{100}\right)+x=\frac{2}{3}\)
\(\frac{99}{100}+x=\frac{2}{3}\)
\(x=\frac{2}{3}-\frac{99}{100}\)
\(x=\frac{200-297}{300}\)
\(x=-\frac{97}{300}\)
b.
\(\left(\frac{2}{11\times13}+\frac{2}{13\times15}+...+\frac{2}{19\times21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)+\frac{221}{231}-x=\frac{4}{3}\)
\(\left(\frac{1}{11}-\frac{1}{21}\right)+\frac{221}{231}-x=\frac{4}{3}\)
\(\left(\frac{21-11}{231}\right)+\frac{221}{231}-x=\frac{4}{3}\)
\(\frac{10}{231}+\frac{221}{231}-x=\frac{4}{3}\)
\(\frac{231}{231}-x=\frac{4}{3}\)
\(1-x=\frac{4}{3}\)
\(x=1-\frac{4}{3}\)
\(x=\frac{3-4}{3}\)
\(x=-\frac{1}{3}\)
Chúc bạn học tốt
\(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}-x+\frac{221}{231}=\frac{4}{3}\)
\(=2\left(\frac{1}{11.13}+\frac{1}{13.15}+...+\frac{1}{19.21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
\(=2.\frac{1}{2}\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
\(=\left(\frac{1}{11}-\frac{1}{21}\right)-x+\frac{221}{231}=\frac{4}{3}\)
\(=\frac{10}{231}-x+\frac{221}{231}=\frac{4}{3}\)
\(\frac{10}{231}-x=\frac{4}{3}-\frac{221}{231}\)
\(\frac{10}{231}-x=\frac{29}{77}\)
\(x=\frac{10}{231}-\frac{29}{77}\)
\(x=\frac{-1}{3}\)
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)-x+4=\frac{7}{3}-\frac{221}{231}\)
\(\left(\frac{1}{11}-\frac{1}{21}\right)-x+4=\frac{106}{77}\)
\(\frac{10}{231}-x=\frac{106}{77}-4\)
\(\frac{10}{231}-x=-\frac{202}{77}\)
\(x=\frac{10}{231}-\left(-\frac{202}{77}\right)\)
\(x=\frac{8}{3}\)
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\Rightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\frac{10}{231}-x+4+\frac{221}{231}=\frac{7}{3}\)
\(\frac{10}{231}-x+4=\frac{7}{3}-\frac{221}{231}\)
\(\frac{10}{231}-x+4=\frac{106}{77}\)
\(\frac{10}{231}-x=\frac{106}{77}-4\)
\(\frac{10}{231}-x=\frac{-202}{77}\)
\(x=\frac{10}{231}-\frac{-202}{77}\)
\(x=\frac{8}{3}\)
a)\(\frac{5}{7}:X=1-\frac{4}{7}=\frac{3}{7}\)
\(X=\frac{5}{7}:\frac{3}{7}=\frac{5}{3}\)
b)
\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{14}+...+\frac{1}{19}-\frac{1}{21}\right)-X=\frac{4}{3}-\frac{221}{231}=\frac{29}{77}\)
\(\left(\frac{1}{11}-\frac{1}{21}\right)-X=\frac{29}{77}\)
\(X=\frac{10}{231}-\frac{29}{77}=-\frac{1}{3}\)
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