(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

= 1/ 2 ( 1/1.2 - 1/2.3 +1/2.3-1/3.4+...+1/8.9-1/9.10 ) x = 22/45

= 1/2 .(1/2-1/90)x = 22/45

= 1/2 . 22/45. x=22/45

x = 22/45:( 22/45 .1/2)

x =2 

duyệt

\(\left(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+...+\frac{1}{8\cdot9\cdot10}\right)x=\frac{23}{45}\)

=> \(\left[\frac{1}{2}\left(\frac{2}{1\cdot2\cdot3}+\frac{2}{2\cdot3\cdot4}+...+\frac{2}{8\cdot9\cdot10}\right)\right]x=\frac{23}{45}\)

=>\(\left[\frac{1}{2}\left(\frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{2\cdot3}-\frac{1}{3\cdot4}+...+\frac{1}{8\cdot9}-\frac{1}{9\cdot10}\right)\right]x=\frac{23}{45}\)

=> \(\left[\frac{1}{2}\left(\frac{1}{2}-\frac{1}{9\cdot10}\right)\right]x=\frac{23}{45}\)

=> \(\left[\frac{1}{2}\cdot\frac{22}{45}\right]x=\frac{23}{45}\)

=> \(\frac{11}{45}x=\frac{23}{45}\)

=> \(x=\frac{23}{45}:\frac{11}{45}=\frac{23}{45}\cdot\frac{45}{11}=\frac{23}{11}\)

Vậy x = 23/11

Ez :))

Lời giải:

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

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

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

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

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

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

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

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

(1/1.2.3 + 1/2.3.4 + ... + 1/8.9.10).x = 23/45

(2/1.2.3 + 2/2.3.4 + ... + 2/8.9.10).x = 2.23/45

(1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + ... + 1/8.9 - 1/9.10).x = 46/45

(1/1.2 - 1/9.10).x = 46/45

(1/2 - 1/90).x = 46/45

(45/90 - 1/90).x = 46/45

22/45.x = 46/45

x = 46/45 : 22/45

x = 46/45 . 45/22

x = 23/11

=2.(1/1-1/2-1/3+1/2-1/3-1/4+...+1/8-1/9-1/10).x=2.23/45

=(1/1-1/10).x=46/45

=9/10.x=46/45

=x=46/45:9/10

=x=92/81:2=46/81.

k cho mình nha!!!"

[1/3 . (1/1.2 - 1/2.3) + 1/3 . (1/2.3 - 1/3.4) +....+ 1/3 . (1/8.9 - 1/9.10)] . x = 23/45

[ 1/3. ( 1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + ...+1/8.9 - 1/9.10)].x = 23/45

[1/3 . (1/1.2 - 1/9.10 )].x = 23/45

( 1/3 . 22/45).x = 23/45

22/135 . x =23/45

x= 23/45 : 22/135

x= 23/45. 135/22

x=69/22

mong cac ban ung ho minh nha