Question

(1/1.2 +1/2.3 1/3.4 + ....+1/8.9) x=23/45

Answer 1

giup mik vs

 

 

Answer 2

Đặt A bằng biểu thức trong ngoặc

\(2A=\dfrac{3-1}{1.2.3}+\dfrac{4-2}{2.3.4}+\dfrac{5-3}{3.4.5}+...+\dfrac{10-8}{8.9.10}\)

\(2A=\dfrac{1}{2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+...+\dfrac{1}{8.9}-\dfrac{1}{9.10}=\dfrac{1}{2}-\dfrac{1}{9.10}\)

\(2A=\dfrac{44}{90}\)

\(A=\dfrac{22}{90}\)

Answer 3

Ta có: \(\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{8\cdot9}\right)\cdot x=\dfrac{23}{45}\)

\(\Leftrightarrow x\cdot\left(1-\dfrac{1}{9}\right)=\dfrac{23}{45}\)

\(\Leftrightarrow x=\dfrac{23}{45}:\dfrac{8}{9}=\dfrac{23}{45}\cdot\dfrac{9}{8}=\dfrac{23}{40}\)