P=2(1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)

P=2((1/2*3)+(1/3*4)+(1/4*5)+(1/5*6)+(1/6*7)+(1/7*8)+(1/8*9)+(1/9*10)

P=2(1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)

P=2(1/2-1/10)

P=2*2/5

P=4/5

H NHA.

\(F=\dfrac{5}{6}+6\dfrac{5}{6}\left(11\dfrac{5}{20}-9\dfrac{1}{4}\right):8\dfrac{1}{3}\)

\(F=\dfrac{5}{6}+\dfrac{41}{6}\left(\dfrac{225}{20}-\dfrac{37}{4}\right):\dfrac{25}{3}\)

\(F=\dfrac{5}{6}+\dfrac{41}{6}.2.\dfrac{3}{25}\)

\(F=\dfrac{5}{6}+\dfrac{41}{25}.\dfrac{3}{25}\)

\(F=\dfrac{5}{6}+\dfrac{41}{25}\)

\(F=\dfrac{371}{150}\)

\(D=\left(\dfrac{136}{15}-\dfrac{28}{5}+\dfrac{62}{10}\right)\times\dfrac{21}{24}\)

\(D=\left(\dfrac{272}{30}-\dfrac{168}{30}+\dfrac{186}{30}\right)\times\dfrac{21}{24}\)

\(D=\dfrac{290}{30}\times\dfrac{21}{24}\)

\(D=\dfrac{29}{3}\times\dfrac{7}{8}\)

\(D=\dfrac{203}{24}\)

\(\frac{1}{2}\) E= \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}\)

\(\frac{1}{2}\) E = \(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{8.9}\)

\(\frac{1}{2}E\) = \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{8}-\frac{1}{9}\)

\(\frac{1}{2}E\) = \(\frac{1}{2}-\frac{1}{9}\)

\(\frac{1}{2}E\) =\(\frac{7}{18}\)

=> E = \(\frac{7}{9}\)

E=\(\frac{1}{3}+\frac{1}{6}+....+\frac{1}{28}+\frac{1}{36}\)

\(\frac{1}{2}E=\frac{1}{6}+\frac{1}{12}+...+\frac{1}{56}+\frac{1}{72}\)

\(\frac{1}{2}E=\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{7.8}+\frac{1}{8.9}\)

\(\frac{1}{2}E=\frac{3-2}{2.3}+\frac{4-3}{3.4}+...\frac{8-7}{7.8}+\frac{9-8}{8.9}\)

\(\frac{1}{2}E=\frac{3}{2.3}-\frac{2}{2.3}+\frac{4}{3.4}-\frac{3}{3.4}+...+\frac{8}{7.8}-\frac{7}{7.8}+\frac{9}{8.9}-\frac{8}{8.9}\)

\(\frac{1}{2}E=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{7}-\frac{1}{8}+\frac{1}{8}-\frac{1}{9}\)

\(\frac{1}{2}E=\frac{1}{2}-\frac{1}{9}=\frac{7}{18}\)

E=\(\frac{7}{18}:\frac{1}{2}=\frac{7}{9}\)

7/15 nhé bạn!

đặt A=1/6+1/10+1/15+1/21+1/28+1/36+1/45

A*2=(1/6*+1/10+1/15+1/21+1/28+1/36+1/45)*2

A*2=1/12+1/20+1/30+1/42+1/56+1/72+1/90

A*2=1/3*4+1/4*5+1/5*6+1/6*7+1/7*8+1/8*9+1/9*10

A*2=1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-/8+1/8-1/9+1/9-1/10

A*2=1/3-1/10

A*2=7/30

A=7/30 / 2

A=7/15

\(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}+\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+\frac{1}{45}\)

\(=2.\left(\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+\frac{1}{90}\right)\)

\(=2.\left(\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{9.10}\right)\)

\(=2.\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}\right)\)

\(=2.\left(\frac{1}{3}-\frac{1}{10}\right)\)

\(=2.\left(\frac{10}{30}-\frac{3}{30}\right)\)

\(=2.\frac{7}{30}\)

\(=\frac{7}{15}\)

Chúc bạn học tốt !!! 

\(\frac{4}{5}\)

đặt A=1/6+1/10+1/15+1/21+1/28+1/36+1/45

6A=1+3/5+2/5+2/7+3/14+1/6+2/15

6A=1+1+7/14+1/6+2/15

6A=14/5

A=14/5:6=7/15

Đặt A = 1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45 
Nhân 2 vế với 1/2 để xuất hiện các mẫu là tích của 2 số tự nhiên liên tiếp sau đó áp dụng công thức 1/n.(n + 1) = 1/n - 1/(n + 1) ta có 
1/2.A = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 
1/2.A = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10 
1/2.A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +.......+ 1/8 - 1/9 + 1/9 - 1/10 
1/2.A = 1- 1/10 
1/2.A = 9/10 
=> A = 9/5 

Đặt A = 1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45

Nhân 2 vế với 1/2 để xuất hiện các mẫu là tích của 2 số tự nhiên liên tiếp sau đó áp dụng công thức 1/n.(n + 1) = 1/n - 1/(n + 1) ta có :

1/2.A = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90

1/2.A = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10

1/2.A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +.......+ 1/8 - 1/9 + 1/9 - 1/10

1/2.A = 1- 1/10

1/2.A = 9/10

=> A = 9/5 

Đặt A = 1+1/3+1/6+1/10+1/15+1/21+1/28+1/36+1/45

Nhân 2 vế với 1/2 để xuất hiện các mẫu là tích của 2 số tự nhiên liên tiếp sau đó áp dụng công thức 1/n.(n + 1) = 1/n - 1/(n + 1) ta có :

 1/2.A = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 

1/2.A = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.10

1/2.A = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 +.......+ 1/8 - 1/9 + 1/9 - 1/10

1/2.A = 1- 1/10

1/2.A=9/10

=> A = 9/5 

1 / 6 + 1 / 10  + 1 / 15 + 1 / 21 +  1 / 28 + 1 / 36 + 1 / 45

= 2 / 12 + 2 / 10 + 2 / 30 + 2 / 42  + 2 / 56 + 2 / 72 + 2 / 90

= 2 ( 1 / 3 . 4 + 1 / 4 . 5 + 1 / 5 . 6 + 1 / 6 . 7 + 1 / 7 . 8 + 1 / 8 . 9 + 1 / 9 . 10 )

= 2 .( 1 / 3 - 1 / 4 + 1 / 4 - 1/ 5 + 1 / 5 - 1 / 6 + 1 / 6 - 1 / 7 + 1 / 7 - 1 / 8 + 1 / 8 - 1 / 9 +1 / 9 - 1 / 10)

=2 ( 1 / 3 - 1 / 10 )

= 2. 7 / 30

= 7 / 15