Ta có: \(x-\frac{20}{11\cdot13}-\frac{20}{13\cdot15}-...-\frac{20}{53\cdot55}=\frac{3}{11}\)

\(\Leftrightarrow x-10\cdot\left(\frac{2}{11\cdot13}+\frac{2}{13\cdot15}+...+\frac{2}{53\cdot55}\right)=\frac{3}{11}\)

\(\Leftrightarrow x-10\cdot\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{53}-\frac{1}{55}\right)=\frac{3}{11}\)

\(\Leftrightarrow x-10\cdot\left(\frac{1}{11}-\frac{1}{55}\right)=\frac{3}{11}\)

\(\Leftrightarrow x-10\cdot\frac{4}{55}=\frac{3}{11}\)

\(\Leftrightarrow x-\frac{8}{11}=\frac{3}{11}\)

\(\Leftrightarrow x=\frac{3}{11}+\frac{8}{11}\)

\(\Leftrightarrow x=1\)

Vậy \(x=1\)thỏa mãn đề. 

\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)

\(\Rightarrow\frac{1}{2}\left(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x\left(x+1\right)}\right)=\frac{2}{9}.\frac{1}{2}\)

\(\Rightarrow\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{x\left(x+1\right)}=\frac{1}{9}\)

\(\Rightarrow\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{x\left(x+1\right)}=\frac{1}{9}\)

\(\Rightarrow\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{1}{9}\)

\(\Rightarrow\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)

\(\Rightarrow\frac{1}{x+1}=\frac{1}{6}-\frac{1}{9}=\frac{1}{18}\)

\(\frac{1}{x+1}=\frac{1}{18}\Rightarrow18.1=1\left(x+1\right)\)

\(\Rightarrow18=x+1\Rightarrow x=18-1=17\)

Cảm ơn bạn nha!

ban viet sai de bai roi khong phai1/27 ma la1/21

ta co: 1/21+1/28+1/36+...+2/x(x+1)=2/9

      1/21.2+1/28.2+1/36.2+...+2/x(x+1).2=2/9.1/2

     1/42+1/56+1/72+...+1/x(x+1)=1/9

     1/6.7+1/7.8+1/8.9+...+1/x(x+1)=1/9

    1/6-1/7+1/7-1/8+1/8-1/9+...+1/x-1/x+1=1/9

     1/6-1/x+1=1/9(khu lien tiep)

           1/x+1=1/6-1/9

       1/x+1=1/18

=>x+1=18

 =>x=17

khu lien tiep là khu liên tiếp đúng ko bạn, tại bạn đánh ko dấu nên mình ko hiểu

\(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)

\(\frac{1}{2}\left(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x\left(x+1\right)}\right)=\frac{2}{9}\cdot\frac{1}{2}\)

\(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{x\left(x+1\right)}=\frac{1}{9}\)

\(\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+...+\frac{1}{x\left(x+1\right)}=\frac{1}{9}\)

\(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{1}{9}\)

\(\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)

\(\frac{1}{x+1}=\frac{1}{6}-\frac{1}{9}\)

\(\frac{1}{x+1}=\frac{1}{18}\)

\(\Rightarrow x+1=18\)

\(x=18-1\)

\(x=17\)

sửa đề số cuối vế trái là \(\frac{1}{x\left(x+1\right)}\)

Đặt A là vế trái

\(\frac{1}{2}A=\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{x\left(x+1\right)}\)

\(=\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{x\left(x+1\right)}\)

\(=\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}+...-\frac{1}{x}+\frac{1}{x}-\frac{1}{x+1}\)

\(=\frac{1}{6}-\frac{1}{x+1}\)

\(\Rightarrow A=\frac{1}{3}-\frac{2}{x+1}=\frac{2}{9}\)

\(\frac{2}{x+1}=\frac{1}{3}-\frac{2}{9}=\frac{1}{9}=\frac{2}{18}\)

\(\Rightarrow x+1=18\Rightarrow x=17\)

Vậy x=17

bạn Nga Nguyễn làm sai rồi , đề bài này hoàn toàn đúng , vì :

\(\frac{2}{x\left(x+1\right)}\cdot\frac{1}{2}=\frac{2\cdot1}{x\left(x+1\right)\cdot2}=\frac{1}{x\left(x+1\right)}\)

còn nếu theo cách của bạn , sẽ ra :

\(\frac{1}{x\left(x+1\right)}\cdot\frac{1}{2}=\frac{1}{x\left(x+1\right)\cdot2}\)

sai nhưng kết quả đúng ? đkp

Sửa đề :v hình như vậy mới làm được

\(2\frac{2}{9}-x=\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}\)

\(\frac{20}{9}-x=\frac{2}{12}+\frac{2}{20}+\frac{2}{30}+\frac{2}{42}+\frac{2}{56}+\frac{2}{72}\)

\(\frac{20}{9}-x=2\left[\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\right]\)

\(\frac{20}{9}-x=2\left[\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}\right]\)

\(\frac{20}{9}-x=2\left[\frac{1}{3}-\frac{1}{9}\right]\)

\(\frac{20}{9}-x=2\cdot\frac{2}{9}\)

\(\frac{20}{9}-x=\frac{4}{9}\Leftrightarrow x=\frac{16}{9}\)

Bạn ơi, mình cũng nghe là sai đề. Nhưng trong đề cương của mình đề 100% nó như vậy ạ.

Ko biết có phải do đề hay ko. :v

=14/15*20/21*...*209/210

\(=\dfrac{4\cdot7}{5\cdot6}\cdot\dfrac{5\cdot8}{6\cdot7}\cdot...\cdot\dfrac{19\cdot22}{20\cdot21}\)

\(=\dfrac{4\cdot5\cdot6\cdot...\cdot19}{5\cdot6\cdot7\cdot...\cdot20}\cdot\dfrac{7\cdot8\cdot9\cdot...\cdot22}{6\cdot7\cdot8\cdot...\cdot21}=\dfrac{11}{15}\)