\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-...+\frac{1}{8}-\frac{1}{9}+\frac{1}{9}-\frac{1}{10}\cdot x=\frac{22}{45}\)

\(\Rightarrow1-\frac{1}{10}.x=\frac{22}{45}\)

\(\Rightarrow\frac{9}{10}.x=\frac{22}{45}\)

\(\Rightarrow x=\frac{22}{45}:\frac{9}{10}\)

\(\Rightarrow x=\frac{22}{45}.\frac{10}{9}=\frac{22.10}{45.9}=\frac{44}{81}\)

=>x=\(\frac{44}{81}\)

(1/1.2.3+1/2.3.4+...+1/8.9.10).x=22/45

<=>(2/1.2.3+2/2.3.4+...+2/8.9.10).x=44/45

<=>(1/1.2-1/2.3+1/2.3-1/3.4+...+1/8.9-1/9.10).x=44/45

<=>(1/1.2-1/9.10).x=44/45

<=>22/45.x=44/45

<=>x=2

vậy x=2 

\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+.............+\frac{1}{8.9.10}\right)x=\frac{22}{45}\)

\(\Rightarrow\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+.........+\frac{2}{8.9.10}\right)x=\frac{22}{45}\)

\(\Rightarrow\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+............+\frac{1}{8.9}-\frac{1}{9.10}\right)x=\frac{22}{45}\)

\(\Rightarrow\frac{1}{2}.\left(\frac{1}{1.2}-\frac{1}{9.10}\right)x=\frac{22}{45}\)

\(\Rightarrow\frac{1}{2}.\frac{22}{45}.x=\frac{22}{45}\)

\(\Rightarrow\frac{11}{45}.x=\frac{22}{45}\)

\(\Rightarrow x=\frac{22}{45}:\frac{11}{45}\)

\(\Rightarrow x=2\)

Mình đồng ý với cách làm của cả hai bạn , nhưng mình thấy bạn Nguyễn Hung Phát làm rõ ràng hơn!!!

\(pt\Leftrightarrow\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+....+\frac{1}{8.9}-\frac{1}{9.10}\right)x=\frac{22}{45}\)

\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{9.10}\right)x=\frac{22}{45}\)

\(\Leftrightarrow\frac{1}{2}.\frac{22}{45}.x=\frac{22}{45}\)

\(\Leftrightarrow\frac{1}{2}x=1\)

\(\Rightarrow x=2\)

Câu hỏi của Kudo Shinichi - Toán lớp 6 - Học toán với OnlineMath

Tham khảo tại link trên chỉ cần nhấn vào .

Chúc bạn học tốt

              \(2Z=\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{8.9.10}\) 

              \(2Z=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}\)

              \(2Z=\frac{1}{1.2}-\frac{1}{9.10}\)

              \(2Z=\frac{22}{45}\)

               \(\Rightarrow\frac{22}{45}.x=\frac{22}{45}\)

                              \(x=\frac{22}{45}:\frac{22}{45}\)

                              \(x=1\)

Lời giải:

Đặt $A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{8.9.10}$

$2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+....+\frac{2}{8.9.10}$

$=\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+...+\frac{10-8}{8.9.10}$

$=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{8.9}-\frac{1}{9.10}$

$=\frac{1}{1.2}-\frac{1}{9.10}=\frac{22}{45}$

$A=\frac{11}{45}$

$Ax=\frac{11}{45}x=\frac{22}{45}$

$x=\frac{22}{45}: \frac{11}{45}=2$

\(\left(\frac{1}{1}-\frac{1}{2}-\frac{1}{3}+\frac{1}{2}-.........+\frac{1}{8}-\frac{1}{9}-\frac{1}{10}\right)\).x = \(\frac{22}{45}\)

 \(\left(1-\frac{1}{10}\right).x=\frac{22}{45}\)

 \(\frac{9}{10}.x=\frac{22}{45}\)

\(x=\frac{22}{45}:\frac{9}{10}\)

\(x=\frac{44}{81}\)

\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right).x=\frac{22}{45}\)

\(\Leftrightarrow\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{8.9.10}\right).x=\frac{44}{45}\)

(Bạn lưu ý chỗ này thì 2 nhân tử ở đầu và cuối của mẫu số cách nhau bao nhiêu đơn vị thì tử là bấy nhiêu nhé )

\(\Leftrightarrow\left(1-\frac{1}{2}+\frac{1}{3}+\frac{1}{2}-\frac{1}{3}+\frac{1}{4}+...+\frac{1}{8}-\frac{1}{9}+\frac{1}{10}\right)x=\frac{44}{45}\)

\(\Leftrightarrow\left(1+\frac{1}{10}\right).x=\frac{44}{45}\)

\(\Leftrightarrow\frac{11x}{10}=\frac{44}{45}\)

\(\Leftrightarrow x=\frac{8}{9}\)

nhấn vào đúng 0 sẽ ra đáp án

Đặt A=11.2.3+12.3.4+....+18.9.10A=11.2.3+12.3.4+....+18.9.10

2A=21.2.3+22.3.4+....+28.9.102A=21.2.3+22.3.4+....+28.9.10

=3−11.2.3+4−22.3.4+...+10−88.9.10=3−11.2.3+4−22.3.4+...+10−88.9.10

=11.2−12.3+12.3−13.4+...+18.9−19.10=11.2−12.3+12.3−13.4+...+18.9−19.10

=11.2−19.10=2245=11.2−19.10=2245

A=1145A=1145

Ax=1145x=2245Ax=1145x=2245

x=2245:1145=2