Đặt A = 9/4  + 9/28 +.. + 9/550

       A = 9/1.4 + 9/4.7 +... + 9/22.25

       A = 3( 3/1.4 + 3/4.7 + .. + 3/22.25)

        A  = 3 . (1/1 - 1/4 + 1/4  - 1/7 + ... +1/22 - 1/25)

         A = 3 (1 - 1/25)

       A   = 3. 24 / 25

       A   =  72/25

dùm e đi ạ :v

đề sai e ưi

sửa ik e

\(\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{3}{130}+....+\frac{3}{418}+\frac{3}{550}\)

\(\Leftrightarrow\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+...+\frac{3}{19.22}+\frac{3}{22.25}\)

\(\Leftrightarrow\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{19}-\frac{1}{22}+\frac{1}{22}-\frac{1}{25}\)

\(\Leftrightarrow\frac{1}{1}-\frac{1}{25}=\frac{24}{25}\)

Nhớ k cho m nhé!

a)

 \(\frac{{28}}{9} \cdot 0,7 + \frac{{28}}{9} \cdot 0,5 = \frac{{28}}{9}.\left( {0,7 + 0,5} \right)\)

b)

\(\begin{array}{l}\frac{{36}}{{13}}:4 + \frac{{36}}{{13}}:9\\ = \frac{{36}}{{13}}.\frac{1}{4} + \frac{{36}}{{13}}.\frac{1}{9}\\ = \frac{{36}}{{13}}.\left( {\frac{1}{4} + \frac{1}{9}} \right)\\ = \frac{{36}}{{13}}.\frac{{13}}{{36}} = 1\end{array}\)

 \(\begin{array}{l}\frac{{36}}{{13}}:(4 + 9)\\ = \frac{{36}}{{13}}:13\\ = \frac{{36}}{{13}}.\frac{1}{{13}}\\ = \frac{{36}}{{169}}\end{array}\)

Suy ra \(\frac{{36}}{{13}}:4 + \frac{{36}}{{13}}:9\) \( \ne \) \(\frac{{36}}{{13}}:(4 + 9)\).

a) $\frac{4}{7} = \frac{{4 \times 2}}{{7 \times 2}} = \frac{8}{{14}}$

Quy đồng mẫu số hai phân số $\frac{9}{{14}}$ và $\frac{4}{7}$ được $\frac{9}{{14}}$ và $\frac{8}{{14}}$

b) $\frac{8}{3} = \frac{{8 \times 3}}{{3 \times 3}} = \frac{{24}}{9}$

Quy đồng mẫu số hai phân số $\frac{{25}}{9}$ và $\frac{8}{3}$ được $\frac{{25}}{9}$ và $\frac{{24}}{9}$

c) $\frac{6}{7} = \frac{{6 \times 10}}{{7 \times 10}} = \frac{{60}}{{70}}$

Quy đồng mẫu số hai phân số $\frac{6}{7}$ và $\frac{9}{{70}}$ được $\frac{{60}}{{70}}$ và $\frac{9}{{70}}$

Lướt qua rồi! không phải bạn k mà ấn tượng "đừng lướt qua"

\(A=\frac{3a}{4.1}+\frac{3a}{7.4}+\frac{3a}{10.7}+\frac{3a}{13.10}+..+\frac{3a}{22.19}+\frac{3a}{25.22}=\frac{48}{25}\)

\(a.\left(\frac{3}{4.1}+\frac{3}{7.4}+\frac{3}{10.7}+\frac{3}{13.10}+..+\frac{3}{22.19}+\frac{3}{25.22}\right)=\frac{48}{25}\)

\(B=\left(\frac{3}{4.1}+\frac{3}{7.4}+\frac{3}{10.7}+\frac{3}{13.10}+..+\frac{3}{22.19}+\frac{3}{25.22}\right)\)

\(B=\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+..+\frac{1}{22}-\frac{1}{25}\)

\(B=\frac{1}{1}-\frac{1}{25}=\frac{24}{25}\)

\(A=a.B=\frac{24a}{25}=\frac{48}{25}\Rightarrow a=2\)

\(\frac{3a}{4}+\frac{3a}{28}+\frac{3a}{70}+...+\frac{3a}{418}+\frac{3a}{550}=\frac{48}{25}\)

\(\Rightarrow a\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{19.22}+\frac{3}{22.25}\right)=\frac{48}{25}\)

\(\Rightarrow a\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{19}-\frac{1}{22}+\frac{1}{22}-\frac{1}{25}\right)=\frac{48}{25}\)

\(\Rightarrow a\left(1-\frac{1}{25}\right)=\frac{48}{25}\)

\(\Rightarrow a.\frac{24}{25}=\frac{48}{25}\)

\(\Rightarrow a=2\)

\(A=\frac{13}{28}\left(-\frac{5}{9}-\frac{4}{9}\right)=\frac{13}{28}\left(-\frac{9}{9}\right)=\frac{13}{28}\left(-1\right)\)

=> \(A=-\frac{13}{28}\)

A= -5/9x 13/28- 13/28x 4/9

  =13/28x (-5/9- 4/9)

  =13/28x (-1)

  =-13/28

a) $\frac{7}{9} \times \frac{{15}}{{28}} \times \frac{9}{7} = (\frac{7}{9} \times \frac{9}{7}) \times \frac{{15}}{{28}} = 1 \times \frac{{15}}{{28}} = \frac{{15}}{{28}}$

b) $\frac{9}{{32}} \times \left( {\frac{2}{3} \times \frac{{14}}{{21}}} \right) = \frac{9}{{32}} \times \left( {\frac{2}{3} \times \frac{2}{3}} \right) = \frac{9}{{32}} \times \frac{4}{9} = \frac{{36}}{{288}} = \frac{1}{8}$