ta có: 

A= 1/6+1/12+1/20+1/30+1/42+1/56

= 1/2.3+1/3.4+1/4.5+1/5.6+1/6.7+1/7.8

= 1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8

= 1/2-1/8

= 3/8

vậy A= 3/8

TA CÓ: 

A=3/8 ban nha k cho minh voi

a: \(=\dfrac{1}{2}\cdot\dfrac{3}{4}\cdot\dfrac{5}{6}=\dfrac{15}{48}=\dfrac{5}{16}\)

b: \(=\dfrac{2}{3}+\dfrac{12}{42}=\dfrac{2}{3}+\dfrac{2}{7}=\dfrac{20}{21}\)

c: \(=\dfrac{24}{5}\cdot\dfrac{5}{12}=2\)

d: \(=\dfrac{1}{9}+\dfrac{3}{4}=\dfrac{4+27}{36}=\dfrac{31}{36}\)

B = 1/6 + 1/12 + 1/20 + ... + 1/90

B = 1/2.3 + 1/3.4 + 1/4.5 + ... + 1/9.10

B = 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + ... + 1/9 - 1/10

B = 1/2 - 1/10

B = 5/10 - 1/10

B = 4/10 = 2/5

Ủng hộ mk nha ♡_♡☆_☆

\(A=\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}\)

\(3A=3\left(\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}+\frac{1}{972}\right)\)

\(3A=\frac{3}{4}+\frac{3}{12}+\frac{3}{36}+\frac{3}{108}+\frac{3}{324}+\frac{3}{927}\)

\(3A=\frac{3}{4}+\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}\)

\(2A=3A-A\)

\(2A=\left(\frac{3}{4}+\frac{1}{4}+\frac{1}{12}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}\right)-\left(\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+\frac{1}{108}+\frac{1}{324}+\frac{1}{972}\right)\)

\(2A=\frac{3}{4}-\frac{1}{927}\)

\(2A=\frac{729-1}{972}=\frac{728}{972}=\frac{182}{243}\)

\(A=\frac{182}{243}:\frac{1}{2}\)

\(A=\frac{364}{243}\)

A=1/4+1/12+1/36+1/108+1/324+1/972

=243/972+81/972+27/972+9/972+3/972+1/972

=364/972

=91/243

\(B=\frac{1}{2}+\frac{5}{6}+\frac{11}{12}+\frac{19}{20}+\frac{29}{30}+\frac{41}{42}+\frac{55}{56}\)

\(B=\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+\left(1-\frac{1}{12}\right)+\left(1-\frac{1}{20}\right)+\left(1-\frac{1}{30}\right)+\left(1-\frac{1}{42}\right)+\left(1-\frac{1}{56}\right)\)

\(B=1.9-\left(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{56}\right)\)

\(B=9-\left[\left(1-\frac{1}{2}\right)+\left(1-\frac{1}{6}\right)+...+\left(1-\frac{1}{56}\right)\right]\)

\(B=9-\left(1-\frac{1}{56}\right)\)

\(B=9-\frac{55}{56}\)

\(B=\frac{449}{56}\)

1: \(=\dfrac{3}{8}\cdot\dfrac{5}{6}=\dfrac{15}{24}=\dfrac{5}{8}\)

2: \(=\dfrac{2}{3}+\dfrac{12}{42}=\dfrac{2}{3}+\dfrac{2}{7}=\dfrac{14+6}{21}=\dfrac{20}{21}\)

3: \(=\dfrac{24}{5}\cdot\dfrac{5}{12}=2\)

4: \(=\dfrac{1}{3}+\dfrac{3}{4}=\dfrac{4+9}{12}=\dfrac{13}{12}\)

`1/2xx3/4:6/5= 1/2 xx 3/4 xx 5/6 = 3/8 xx 5/6 =5/16`           

`2/3+1/6:7/12 = 2/3 + 1/6 xx 12/7 = 2/3 + 2/7 = 14/21 + 6/21 = 20/21`       

`8xx3/5:12/5= 8xx 3/5 xx 5/12 = 24/5 xx 5/12 = 2`         

`4/9+3/4-1/3= (16/36 + 27/36 ) - 1/3 = 43/36 - 1/3 = 31/36`

`1/2xx3/4:6/5`

`=1/2xx3/4xx5/6`

`=3/8xx5/6`

`=15/48`

`=5/16`

__

`2/3+1/6:7/12`

`=2/3+1/6xx12/7`

`=2/3+2/7`

`=14/21+6/21`

`=20/21`

__

`8xx3/5:12/5`

`=8xx3/5xx5/12`

`=8xx1/4`

`=8/4`

`=2`

__

`4/9+3/4-1/3`

`=(4/9-1/3)+3/4`

`=(4/9-3/9)+3/4`

`=1/9+3/4`

`=4/36+27/36`

`=31/36`

a) \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\)

\(=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\) (dấu chấm là dấu nhân)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\)

\(=1-\frac{1}{7}\)

\(=\frac{6}{7}\)

b) \(\frac{19}{13}+\frac{14}{6}+\frac{1}{9}+\frac{4}{6}+\frac{7}{13}+\frac{17}{9}\)

\(=\left(\frac{19}{13}+\frac{7}{13}\right)+\left(\frac{14}{6}+\frac{4}{6}\right)+\left(\frac{1}{9}+\frac{17}{9}\right)\)

= 2 + 3 + 2

= 7