\(\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+....+\frac{1}{19.21}\right).x=\frac{9}{7}\)

\(\left(\frac{5-3}{3.5}+\frac{7-5}{5.7}+\frac{9-7}{7.9}+...+\frac{21-19}{19.21}\right).x=\frac{9}{7}\)

\(\left[\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\right)\right].x=\frac{9}{7}\)

 \(\left[\frac{1}{2}.\left(\frac{1}{3}-\frac{1}{21}\right)\right].x=\frac{9}{7}\)

 \(\left[\frac{1}{2}.\frac{2}{7}\right].x=\frac{9}{7}\)

\(\frac{1}{7}.x=\frac{9}{7}\)

\(\Rightarrow x=\frac{9}{7}\div\frac{1}{7}=9\)

\(\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{19.21}\right)x=\frac{9}{7}\)

\(\Leftrightarrow\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{19}-\frac{1}{21}\right)x=\frac{9}{7}\)

\(\Leftrightarrow\left(\frac{1}{3}-\frac{1}{21}\right)x=\frac{9}{7}\)

\(\Leftrightarrow\frac{2}{7}x=\frac{9}{7}\)

\(\Leftrightarrow x=\frac{9}{2}\)

2 ( 1/3.5 + 1/5.7 + 1/7.9+......+ 1/19.21) . x = 2.9/7

 (2/3.5 + 2/5.7 + 2/7.9+......+ 2/19.21). x = 18/7

(1/3-1/5 + 1/5-1/7+ 1/7-1/9 +.....+ 1/19 - 1/21).x = 18/7

(1/3-1/21) . x= 18/7

2/7 x = 18/7

x= 18/7 . 7/2

x= 9

\(\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{8.9.10}\right).x=\frac{23}{45}\)

\(\frac{1}{2}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+...+\frac{2}{8.9.10}\right).x=\frac{23}{45}\)

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

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

\(\frac{1}{2}.\frac{22}{45}.x=\frac{23}{45}\)

         \(\frac{11}{45}.x=\frac{23}{45}\)

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

                 \(x=\frac{23}{11}\)

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

    2A=3-1/1.2.3+ 4–2/2.3.4+ 5–4/3.4.5+ ... + 10–8/8.9.10

    2A=1/2 —1/2.3+ 1/2.3 — 1/3.4+ 1/3.4– 1/4.5 +...+1/8.9–1/9.10=1/2–1/9.10=44/90

     A=44/90 : 2=22/90

     x=23/45:A= 23/45 : 22/90=23/11= 2 1/1( hỗn số)

Nhầm đáp án là 2 1/11 nhé

hình như bài này là dạng chuỗi

Bước 1: \(\left(\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+...+\frac{1}{19\times21}\right)=\frac{1}{7}\)

Bước 2: \(x=\frac{9}{7}\div\frac{1}{7}=9\)

b)

\(x-2.\left(\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}\right)=\frac{16}{9}\)

\(x-2\cdot\left(\frac{1}{3}-\frac{1}{9}\right)=\frac{16}{9}\)

\(x-2=\frac{16}{9}:\left(\frac{1}{3}-\frac{1}{9}\right)\)

\(x-2=8\)

=> x = 10

a) 

\(A=\frac{1}{2}.\frac{2}{3}\cdot\frac{3}{4}\cdot\cdot\cdot\frac{2013}{2014}\cdot\frac{2014}{2015}\cdot\frac{2015}{2016}\)

\(A=\frac{1}{2016}\)

A = ( 1 - 1/2) . ( 1 - 1/3 ) . (1-1/4) ....(1-1/2015) . (1-1/2016)

A= 1/2 . 2/3 . 3/4...2014/2015 . 2015/2016

A = 1 . 2 . 3 . 4 ... 2014 . 2015/ 2 . 3 . 4 ... 2015 . 2016

A = 1/ 2016

a) 

( 4x - 9 ) ( 2,5 + (-7/3) . x ) = 0

\(\Rightarrow\orbr{\begin{cases}4x-9=0\\2,5+\frac{-7}{3}x=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=\frac{9}{4}\\x=\frac{15}{14}\end{cases}}\)

P/s: đợi xíu làm câu b

b) \(\frac{1}{x\left(x+1\right)}\cdot\frac{1}{\left(x+1\right)\left(x+2\right)}\cdot\frac{1}{\left(x+2\right)\left(x+3\right)}-\frac{1}{x}=\frac{1}{2015}\)

\(\frac{1}{x}-\frac{1}{x+1}+\frac{1}{x+1}-\frac{1}{x+2}+\frac{1}{x+2}-\frac{1}{x+3}-\frac{1}{x}=\frac{1}{2015}\)

\(\frac{-1}{x+3}=\frac{1}{2015}\)

\(\Leftrightarrow x+3=-2015\)

\(\Leftrightarrow x=-2018\)

Vậy,.........

A/ Ta có số nào nhân với 0 cx = 0 

Vậy từ đó suy ra 2 trường hợp 

TH1\(4x-9=0\)

\(=>x=\frac{9}{4}\)

TH2 \(2,5+-\frac{7}{3}x=0\)

 \(=>x=\frac{15}{14}\)

Trước hết ta thực hiện biểu thức trong ngoặc:

\(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{8.9.10}\)

\(=\frac{1}{2}\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{8.9.10}\right)\)

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

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

\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{90}\right)\)

\(=\frac{1}{2}.\frac{22}{45}\) \(=\frac{11}{45}\)

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

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

\(\Rightarrow x=2\)