a) \(\left(\dfrac{11}{12}+\dfrac{11}{12.23}+\dfrac{11}{23.34}+...+\dfrac{11}{89.100}\right)+x=\dfrac{5}{3}\)

\(\Rightarrow\left(\dfrac{11}{1.12}+\dfrac{11}{12.23}+\dfrac{11}{23.34}+...+\dfrac{11}{89.100}\right)+x=\dfrac{5}{3}\)

\(\Rightarrow\left(1-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{34}+...+\dfrac{1}{89}-\dfrac{1}{100}\right)+x=\dfrac{5}{3}\)

\(\Rightarrow1-\dfrac{1}{100}+x=\dfrac{5}{3}\)

\(\Rightarrow x=\dfrac{5}{3}-1+\dfrac{1}{100}\)

\(\Rightarrow x=\dfrac{500}{300}-\dfrac{300}{300}+\dfrac{3}{300}\)

\(\Rightarrow x=\dfrac{203}{300}\)

b) \(\left(\dfrac{5}{11.16}+\dfrac{5}{16.21}+...+\dfrac{5}{19.24}\right)-x+\dfrac{1}{3}=\dfrac{7}{3}\)

=>\(\left(\dfrac{1}{11}-\dfrac{1}{16}+\dfrac{1}{16}-\dfrac{1}{21}+...+\dfrac{1}{19}-\dfrac{1}{24}\right)-x=\dfrac{7}{3}-\dfrac{1}{3}\)

\(\Rightarrow\dfrac{1}{11}-\dfrac{1}{24}-x=2\)

\(\Rightarrow-x=2-\dfrac{1}{11}+\dfrac{1}{24}\)

\(\Rightarrow-x=\dfrac{528}{264}-\dfrac{24}{264}+\dfrac{11}{264}\)

\(\Rightarrow x=\dfrac{515}{264}\)

c) Câu hỏi của Đàm Chu Hữu An - Toán lớp 6 - Học toán với OnlineMath

1)

a)\(x+\dfrac{3}{22}=\dfrac{27}{121}.\dfrac{11}{9}\)

\(x+\dfrac{3}{22}=\dfrac{3}{11}\)

\(x=\dfrac{6}{22}-\dfrac{3}{22}\)

\(x=\dfrac{3}{22}\)

Ta có : 

\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}\)

\(S=5\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}\right)\)

\(S=5\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}\right)\)

\(S=5\left(1-\frac{1}{26}\right)\)

\(S=5.\frac{25}{26}\)

\(S=\frac{125}{26}\)

Vậy \(S=\frac{125}{26}\)

Chúc bạn học tốt ~ 

S=125/26

a, bạn tự làm 

b, \(B=\dfrac{5^2}{5}\left(1-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{16}+...+\dfrac{1}{101}-\dfrac{1}{106}\right)\)

\(=5\left(1-\dfrac{1}{106}\right)=\dfrac{5.105}{106}=\dfrac{525}{106}\)

c, đk : \(x\ne\dfrac{2}{3}\)

Ta có : \(\left|x-1\right|=2\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\)(tm)

Với x = 3 suy ra \(C=\dfrac{2.9+9-1}{3.3-2}=\dfrac{26}{7}\)

Với x = -1 suy ra \(C=\dfrac{2-3-1}{-3-2}=\dfrac{-2}{-5}=\dfrac{2}{5}\)

C=1/(2x4)+1/(4x6)+...+1/(18x20)

2C=2/(2x4)+2/(4x6)+...+2/(18x20)

2C=1/2-1/4+1/4-1/6+....-1/20

2C= 1/2- 1/20

2C= 9/20

C= 9/20 x 1/2

C= 9/40

- Quên k auto súc vặc

a)

\(\Rightarrow A=\frac{\frac{1}{11}-\frac{1}{13}-\frac{1}{17}}{5\left(\frac{1}{11}-\frac{1}{13}-\frac{1}{17}\right)}+\frac{2\left(\frac{1}{3}-\frac{1}{9}-\frac{1}{27}+\frac{1}{81}\right)}{7\left(\frac{1}{3}-\frac{1}{9}-\frac{1}{27}+\frac{1}{81}\right)}\)

\(\Rightarrow A=\frac{1}{5}+\frac{2}{7}\)

\(\Rightarrow A=\frac{17}{35}\)

b)

\(\Rightarrow B=5\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+....+\frac{1}{56}-\frac{1}{61}\right)\)

\(\Rightarrow B=5\left(\frac{1}{11}-\frac{1}{61}\right)\)

\(\Rightarrow B=5.\frac{50}{671}=\frac{250}{671}\)

c)

\(\Rightarrow C=1-\left(\frac{1}{1.3}+\frac{1}{2.3}+\frac{1}{2.5}+....+\frac{1}{49.25}\right)\)

\(\Rightarrow C=1-2\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+....+\frac{1}{49.50}\right)\)

\(\Rightarrow C=1-2\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{49}-\frac{1}{50}\right)\)

\(\Rightarrow C=1-1-\frac{1}{25}\)

\(\Rightarrow C=\frac{1}{25}\)

a) Đề phải là thế này chứ  \(\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{101.106}\)

                          Giai 

\(=\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{101.106}\)

\(=\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{101}-\frac{1}{106}\)

\(=\frac{1}{6}-\frac{1}{106}\)

\(=\frac{25}{159}\)

b) Đặt \(A=\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{100}}\)

\(\Rightarrow5A=1+\frac{1}{5}+...+\frac{1}{5^{99}}\)

\(\Rightarrow5A-A=\left(1+\frac{1}{5}+...+\frac{1}{5^{99}}\right)-\left(\frac{1}{5}+\frac{1}{5^2}+...+\frac{1}{5^{100}}\right)\)

\(\Rightarrow4A=1-\frac{1}{5^{100}}\)

\(\Rightarrow A=\frac{1-\frac{1}{5^{100}}}{4}\)

\(x+\frac{1}{1.2}+\frac{2}{2.4}+\frac{3}{4.7}+\frac{4}{7.11}+\frac{5}{11.16}=1\)

\(x+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}=1\)

\(x+1-\frac{1}{16}=1\)

\(x+\frac{15}{16}=1\)

\(x=1-\frac{15}{16}\)

\(x=\frac{1}{16}\)