\(A=\dfrac{4}{19.21}+\dfrac{4}{21.23}+\dfrac{12}{23.29}+\dfrac{4}{29.31}\)

\(A=2\left(\dfrac{1}{19}-\dfrac{1}{21}+\dfrac{1}{21}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{29}+\dfrac{1}{29}-\dfrac{1}{31}\right)\)

\(A=2\left(\dfrac{1}{19}-\dfrac{1}{31}\right)\)

Cái này tự tính được,khuay r t lười đi lấy mt lắm

Theo đề ta có:

A=\(\dfrac{4}{19.21}+\dfrac{4}{21.23}+\dfrac{12}{23.29}+\dfrac{4}{29.31}\)

=> 2.(\(\dfrac{2}{19.21}+\dfrac{2}{21.23}+\dfrac{6}{23.29}+\dfrac{2}{29.31}\))

=> 2. \((\dfrac{2}{19.21}+\dfrac{2}{21.23}+\dfrac{2}{29.31})+\dfrac{6}{23.29}\)

=> 2. \(\left(\dfrac{1}{19}+\dfrac{1}{21}-\dfrac{1}{21}+\dfrac{1}{23}+......+\dfrac{1}{29}-\dfrac{1}{31}\right)\)

=> 2.( \(\dfrac{1}{19}-\dfrac{1}{31}\))

=> 2.( \(\dfrac{31}{589}-\dfrac{19}{589}\))

=> 2. \(\dfrac{12}{589}\)

=> \(\dfrac{24}{589}\)

Vậy A= \(\dfrac{24}{589}\)

A = \(\frac{7}{10.11}+\frac{7}{11.12}+\frac{7}{12.13}+...+\frac{7}{69.70}\)

=\(7\left(\frac{1}{10.11}+\frac{1}{11.12}+\frac{1}{12.13}+...+\frac{1}{69.70}\right)\)

=\(7\left(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}+\frac{1}{12}-\frac{1}{13}+...+\frac{1}{69}-\frac{1}{70}\right)\)

=\(7\left(\frac{1}{10}-\frac{1}{70}\right)\)

=\(7.\frac{3}{35}\)

=\(\frac{3}{5}\)

B=\(\frac{1}{25.27}+\frac{1}{27.29}+\frac{1}{29.31}+...+\frac{1}{73.75}\)

=\(\frac{1}{2}\left(\frac{2}{25.27}+\frac{2}{27.29}+\frac{2}{29.31}+...+\frac{2}{73.75}\right)\)

=\(\frac{1}{2}\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+\frac{1}{29}-\frac{1}{31}+...+\frac{1}{73}-\frac{1}{75}\right)\)

=\(\frac{1}{2}\left(\frac{1}{25}-\frac{1}{75}\right)\)

=\(\frac{1}{2}.\frac{2}{75}\)

=\(\frac{1}{75}\)

C : có ở bên dưới rồi, còn A và B thôi

1) A=7(\(\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-......+\frac{1}{69}-\frac{1}{70}\) )

 A=7 ( \(\frac{1}{10}-\frac{1}{70}\))

A=7x 6/70

A=3/5

`A=4/(1.2)+4/(2.3)+4/(3.4)+......+4/(2014.2015)`
`=4(1/(1.2)+1/(2.3)+1/(3.4)+......+1/(2014.2015))`
`=4(1-1/2+1/2-1/3+1/3-1/4+....+1/2014-1/2015)`
`=4(1-1/2015)`
`=4. 2014/2015`
`=8056/2015`

A=4.(1/1.2+1/2.3+...+1/2014.2015)

A=4.(1-1/2+1/2-1/3+...+1/2014-1/2015)

A=4.(1-1/2015)

A=4.2014/2015

A=8056/2015

Giải:

\(A=\dfrac{4}{1.2}+\dfrac{4}{2.3}+\dfrac{4}{3.4}+...+\dfrac{4}{2014.2015}\) 

\(A=4.\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2014.2015}\right)\) 

\(A=4.\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2014}-\dfrac{1}{2015}\right)\) 

\(A=4.\left(\dfrac{1}{1}-\dfrac{1}{2015}\right)\) 

\(A=4.\dfrac{2014}{2015}\) 

\(A=\dfrac{8056}{2015}\)

a)

\(\begin{array}{l}{\left( {1 + \frac{1}{2} - \frac{1}{4}} \right)^2}.\left( {2 + \frac{3}{7}} \right)\\ = {\left( {\frac{4}{4} + \frac{2}{4} - \frac{1}{4}} \right)^2}.\left( {\frac{{14}}{7} + \frac{3}{7}} \right)\\ = {\left( {\frac{5}{4}} \right)^2}.\frac{{17}}{7}\\ = \frac{{25}}{{16}}.\frac{{17}}{7}\\ = \frac{{425}}{{112}}\end{array}\)

b)

\(\begin{array}{l}4:{\left( {\frac{1}{2} - \frac{1}{3}} \right)^3}\\ = 4:{\left( {\frac{3}{6} - \frac{2}{6}} \right)^3}\\ = 4:{\left( {\frac{1}{6}} \right)^3}\\ = 4:\frac{1}{{216}}\\ = 4.216\\ = 864\end{array}\)

a) \(\frac{4}{5}\) của 100 là: \(\frac{4}{5}.100=80\)

b) \(\frac{1}{4}\) của -8 là: \(\frac{1}{4}.(-8)=-2\)

54444

\(b.\frac{1}{3}+\frac{3}{35}< \frac{x}{210}< \frac{4}{7}+\frac{3}{5}+\frac{1}{3}\)

\(\Leftrightarrow\frac{35+9}{105}< \frac{x}{210}< \frac{60+63+35}{105}\)

\(\Leftrightarrow\frac{44}{105}< \frac{x}{210}< \frac{158}{105}\)

\(\Leftrightarrow\frac{88}{210}< \frac{x}{210}< \frac{316}{210}\)

Suy ra \(x\in\left\{89;90;100;...;313;314;315\right\}\)

\(c.\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right)-x+\frac{221}{231}=\frac{4}{3}\)

\(\Leftrightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)-x+\frac{221}{231}=\frac{4}{3}\)

\(\Leftrightarrow\frac{1}{11}-\frac{1}{21}-x+\frac{221}{231}=\frac{4}{3}\)

\(\Leftrightarrow\frac{21-11-231x+221}{231}=\frac{308}{231}\)

\(\Leftrightarrow-231x=308-21+11-221\)

\(\Leftrightarrow-231x=77\)

\(\Leftrightarrow x=-\frac{77}{231}=-\frac{1}{3}\)

^^