Ta có:\(\left(x-1\right)+\left(x-2\right)+...+\left(x-20\right)=-610\)

\(x-1+x-2+x-3+...+x-20=-610\)

\(\left(20x\right)+\left(-1+-2+-3+...+-20\right)=610\)

\(\left(20x\right)+-210=610\)

\(\left(20x\right)-210=610\)

\(20x=610+210\)

\(20x=820\)

\(x=820:20\)

\(x=41\)

\(\dfrac{1}{6}x+\dfrac{1}{12}x+\dfrac{1}{20}x+...+\dfrac{1}{2450}x=1\)

\(x\left(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+...+\dfrac{1}{2450}\right)\)=1

\(x\left(\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+...+\dfrac{1}{49\times50}\right)\)=1

\(x\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\right)=1\)

\(x\left(\dfrac{1}{2}-\dfrac{1}{50}\right)=1\)

\(x\times\)\(\dfrac{12}{25}=1\)

\(\Rightarrow x=1\div\dfrac{12}{25}\)

\(x=1\times\dfrac{25}{12}=\dfrac{25}{12}\)

vậy \(x=\dfrac{25}{12}\)

vậy \(x=2\)\(x=2\)\(\Rightarrow\left(\dfrac{20}{9}-x\right)=\dfrac{1}{3}-\dfrac{1}{9}\)\(\left(2\dfrac{2}{9}-x\right)\)=\(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+...+\dfrac{1}{72}\)

\(\Rightarrow\left(\dfrac{20}{9}-x\right)=\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+...+\dfrac{1}{72}\)\(\Rightarrow\left(\dfrac{20}{9}-x\right)=\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}+...+\dfrac{1}{8\times9}\)\(\Rightarrow\left(\dfrac{20}{9}-x\right)=\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+...+\dfrac{1}{8}-\dfrac{1}{9}\)

nè bn!!!!

máy hết chỗ đánh làm ơn chuyển 3 dòng đầu này xuống cuối

\(\left(\dfrac{20}{9}-x\right)=\dfrac{1}{3}-\dfrac{1}{9}\)

\(\left(\dfrac{20}{9}-x\right)=\dfrac{2}{9}\)

\(x=\dfrac{20}{9}-\dfrac{2}{9}\)

\(x=2\)

vậy x=2

giúp mk nha !!!THANKS!!!

Từ GT ; ta có :  \(\left(x-1\right)\left(\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}\right)=224\)

\(\Rightarrow\left(x-1\right)\left(\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{7.8}+\dfrac{1}{8.9}\right)=224\)

\(\Rightarrow\left(x-1\right)\left(\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}\right)=224\)

\(\Rightarrow\left(x-1\right)\left(\dfrac{1}{3}-\dfrac{1}{9}\right)=224\)

\(\Rightarrow\left(x-1\right).\dfrac{2}{9}=224\)

\(\Rightarrow\left(x-1\right)=1008\)

\(\Rightarrow x=1009\)

Vậy ... 

Phân tích phân số ra 

Mình Đi học đã gợi ý đó

A = 1/90 - 1/72 - 1/56 - 1/42 - 1/30 - 1/20 - 1/12 - 1/6 - 1/2

A = 1/90 - ( 1/72 + 1/56 + 1/42 + 1/30 + 1/20 + 1/12 + 1/6 + 1/2)

A = 1/90 - ( 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72)

A = 1/90 - ( 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9)

A = 1/90 - ( 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/8 - 1/9)

A = 1/90 - ( 1 - 1/9)

 A = 1/90 - 8/9

A = 1/90 - 80/90 = -79/90

A=1/90-1/72-1/56-1/42-1/30-1/20-1/12-1/6-1/2

A=1/90-(1/72+1/56+1/42+1/30+1/20+1/12+1/6+1/2)

A=1/90-(1-1/9)

A=1/90-8/9=1/90-80/90=-79/90

Sửa đề

\(\dfrac{2}{1^2}\cdot\dfrac{6}{2^2}\cdot\dfrac{12}{3^3}\cdot.......\cdot\dfrac{110}{10^2}\cdot x=-20\)

\(\dfrac{2}{1\cdot1}\cdot\dfrac{2\cdot3}{2\cdot2}\cdot\cdot\cdot\cdot\dfrac{11\cdot10}{10\cdot10}\cdot x=-20\)

\(\dfrac{\left(2\cdot3\cdot4\cdot....\cdot11\right)}{\left(1\cdot2\cdot3\cdot4\cdot...\cdot10\right)}\cdot\dfrac{\left(1\cdot2\cdot3\cdot4\cdot5\cdot...\cdot10\right)}{\left(1\cdot2\cdot3\cdot4\cdot...\cdot10\right)}\cdot x=-20\)

\(11\cdot x=-20\\ x=-\dfrac{20}{11}\)

Ko đề cho thêm \(\dfrac{20}{4²}\) mà