Đặt A bằng biểu thức trong ngoặc

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

\(2A=\dfrac{1}{2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+...+\dfrac{1}{8.9}-\dfrac{1}{9.10}=\dfrac{1}{2}-\dfrac{1}{9.10}=\dfrac{44}{90}\)

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

\(x=\dfrac{23}{45}:A=\dfrac{23}{45}:\dfrac{22}{90}=\dfrac{23}{11}=2\dfrac{1}{11}\)

\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\)

\(A=\frac{1}{2}\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+...+\frac{10-8}{8.9.10}\right)\)

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

\(A=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{9.10}\right)=\frac{11}{45}\).

Phương trình tương đương với: 

\(\frac{11}{45}x=\frac{22}{45}\Leftrightarrow x=2\).

\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+.....+\frac{1}{8.9}-\frac{1}{9.10}\right).x=\frac{23}{45}\)

\(\Leftrightarrow\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{9.10}\right).x=\frac{23}{45}\)

\(\Leftrightarrow\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{90}\right).x=\frac{23}{45}\)

\(\Leftrightarrow\frac{1}{2}.\frac{44}{90}.x=\frac{23}{45}\Rightarrow\frac{11}{45}.x=\frac{23}{45}\Rightarrow x=\frac{23}{45}:\frac{11}{45}=\frac{23}{11}\)

Đặt A bằng Biểu thức trong ngoặc

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

\(2A=\frac{1}{2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{8.9}-\frac{1}{9.10}=\frac{1}{2}-\frac{1}{9.10}=\frac{44}{90}\)

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

\(x=\frac{23}{45}:A=\frac{23}{45}:\frac{22}{90}=\frac{23}{11}=2\frac{1}{11}\)

Áp dụng công thức sau mà dải:

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

cho 2a lan thu 2 bn viet t ko hieu.jai lai cho t di

Cô hướng dẫn nhé

a. 5^2x-3=5.5²=5³. Vậy 2x - 3 = 3.

b. \(\frac{30\left(x-5\right)-20x}{100}=5\Rightarrow\frac{10x-150}{100}=5\)

c. Theo công thức tính tổng \(\frac{\left(x+1\right)x}{2}=aaa\Rightarrow x\left(x+1\right)=2a.111\)

Do 111 là số nguyên tố mà a<=9 nên ko tìm được x.

d. Em có thể xem trong bài giảng Tính tổng có quy luật của cô nhé.

(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