\(\dfrac{4}{2\cdot4}+\dfrac{4}{4\cdot6}+\dfrac{4}{6\cdot8}+...+\dfrac{4}{x\left(x+2\right)}=\dfrac{2011}{2013}\)

\(\Leftrightarrow2\left(\dfrac{2}{2\cdot4}+\dfrac{2}{4\cdot6}+\dfrac{2}{6\cdot8}+...+\dfrac{2}{x\left(x+2\right)}\right)=\dfrac{2011}{2013}\)

\(\Leftrightarrow\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{x}-\dfrac{1}{x-2}=\dfrac{2011}{4026}\)

\(\Leftrightarrow\dfrac{1}{2}-\dfrac{1}{x-2}=\dfrac{2011}{4026}\)\(\Leftrightarrow\dfrac{1}{x-2}=\dfrac{1}{2013}\)

\(\Rightarrow x-2=2013\Rightarrow x=2015\)

Gọi biều thức trên là A, ta có:

A=(1/2.4+1/4.6+1/6.8+1/8.10+1/10.12)x=2

2A=(2/2.4+2/4.6+2/6.8+2/8.10+2/10.12)x=2

2A=(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12)x=2

2A=(1/2-1/4+1/4-1/6+1/6-1/8+1/8-1/10+1/10-1/12)x=2

2A=(1/2-1/12)x=2

2A=5/12x=2

=>A=5/24x=1

=>x=1:5/24=24/5

=>1/2.(5/12).x=1

5/24.x=1

x=1:5/24

x=24/5

lưu ý, 1/2.5/12 là tính xong phần 1/2.4 +...+1/10.12 rùi nhé

Trả lời hô mình

2

\(S1=\frac{1}{2.4}+\frac{1}{4.6}+\frac{1}{6.8}+...+\frac{1}{100.102}\)

\(S1=\frac{1}{2}.\left(\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{100.102}\right)\)

\(S1=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{100}-\frac{1}{102}\right)\)

\(S1=\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{102}\right)\)

\(S1=\frac{1}{2}.\left(\frac{51}{102}-\frac{1}{102}\right)\)

\(S1=\frac{1}{2}.\frac{25}{51}\)

\(S1=\frac{25}{102}\)

Ngu Người bạn uống thuốc chữa bênh đi tiểu nhiều lần

J vậy cái ông Phạm Nhật quang kia

\(a,\frac{1}{3}x+\frac{2}{5}x-\frac{2}{5}=0\)

\(\frac{11}{15}x=\frac{2}{5}\)

\(x=\frac{6}{11}\)

b,\(\left(2x-3\right).\left(6-2x\right)=0\)

\(\Rightarrow\orbr{\begin{cases}2x-3=0\\6-2x=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=\frac{3}{2}\\x=3\end{cases}}\)

Vậy

A=(1.2)(2.2)+(2.2)(3.2)+...+(50.2)(51.2)

A=1.2.4+2.3.4+...+50.51.4

A=4(1.2+2.3+...+50.51)

M= 1.2+2.3+...+50.51

3M=1.2.3+2.3.(4-1)+...+50.51.(52-49)

=1.2.3+2.3.4-1.2.3+...+50.51.52-49.50.51

= 50.51.52

=132600

=> M=44200

=> A=4M=176800

\(x-\dfrac{1}{2}\left(\dfrac{2}{2.4}+\dfrac{2}{4.6}+...+\dfrac{2}{98.100}\right)=\dfrac{1}{100}\)

\(x-\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{6}+...+\dfrac{1}{98}-\dfrac{1}{100}\right)=\dfrac{1}{100}\)

\(x-\dfrac{1}{2}\left(\dfrac{1}{2}-\dfrac{1}{100}\right)=\dfrac{1}{100}\)

\(x=\dfrac{51}{200}\)

Xét tử: 2.4+4.8+8.12+12.16+16.20 = 2.1.2.2 + 2.2.2.4 + 2.2.4.6 + 2.2.6.8 + 2.2.8.10

                                                   = 2.2.(1.2+2.4+4.6+6.8+8.10)

=> 2.4+4.8+8.12+12.16+16.20/1.2+2.4+4.6+6.8+8.10 = 2.2.(1.2+2.4+4.6+6.8+8.10) / 1.2+2.4+4.6+6.8+8.10

                                                                               = 2.2 = 4

camon nhan (: