\(\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}\)

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

\(=\dfrac{1}{2}-\dfrac{1}{6}\)

\(=\dfrac{1}{3}\)

* Bạn tham khảo nhé *

1212 ++ 1616 ++ 112112 ++ 120120 ++ 130130 ++ 142142 ++ 156156

== 11×211×2 ++ 12×312×3 ++ 13×413×4 ++ 14×514×5 ++ 15×615×6 ++ 16×716×7 ++ 17×817×8

== 1111 −− 1212 ++ 1212 −− 1313 ++ 1313 −− 1414 ++ 1414 −− 1515 ++ 1515 −− 1616 ++ 1616 −− 1717 ++ 1717 −− 1818

== 1111 −− 1818

== 8888 −− 1818

== 78

misa

Đặt tên biểu thức là A ta có :

\(A=\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+....+\frac{1}{90}+\frac{1}{110}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{10}-\frac{1}{11}\)

\(=\left(\frac{1}{2}-\frac{1}{11}\right)+\left(\frac{1}{3}-\frac{1}{3}\right)+.....+\left(\frac{1}{10}-\frac{1}{10}\right)\)

\(=\left(\frac{1}{2}-\frac{1}{11}\right)+0+......+0\)

\(=\frac{11}{22}-\frac{2}{22}=\frac{9}{22}\)

\(\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+...+\frac{1}{10.11}\)

=\(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}\)

=\(\frac{1}{2}-\frac{1}{11}\)

=\(\frac{9}{22}\)

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{90}+\frac{1}{110}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{9.10}+\frac{1}{10.11}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)

\(=1-\frac{1}{11}\)

\(=\frac{10}{11}\)

\(\frac{1}{2}-\frac{1}{6}-\frac{1}{12}-\frac{1}{20}-\frac{1}{30}=\frac{1}{1\cdot2}-\frac{1}{2\cdot3}-\frac{1}{3\cdot4}-\frac{1}{4\cdot5}-\frac{1}{5\cdot6}\)

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

\(=\frac{1}{1}-\frac{1}{6}=\frac{5}{6}\)

NHỚ K MK NHA. CHÚC BẠN HỌC TỐT

  1/2 - 1/6 - 1/12 - 1/20 - 1/30

=1/1x2 - 1/2x3- 1/3x4 - 1/4x5 - 1/5x6

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

=1-1/6

=5/6

b) 13/17 : 8/3 - 5/17 : 8/3

= ( 13/17 -  5/17 ) : 8/3

= 7/17  *  3/8

=21/136

c) 1/6 + 1/12 + 1/20 + 1/20

= (1/6 + 1/12) + (1/20 + 1/20)

= (2/12 + 1/12) + (1/20 + 1/20)

=  3/12  +  2/20

=  1/4 +2/20

= 5/20 + 2/20

=  7/20

\(b)\frac{13}{17}\div\frac{8}{3}-\frac{5}{17}\div\frac{8}{3}\)

\(=\left(\frac{13}{17}-\frac{5}{17}\right)\div\frac{8}{3}\)

\(=\frac{8}{17}\div\frac{8}{3}\)

\(=\frac{3}{17}\)

\(c)\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{20}\)

\(=\left(\frac{2}{12}+\frac{1}{12}\right)+\left(\frac{1}{20}+\frac{1}{20}\right)\)

\(=\frac{1}{4}+\frac{2}{20}\)

\(=\frac{5}{20}+\frac{2}{20}=\frac{7}{20}\)

(13/17 - 5/17) : 8/3 = 8/17 : 8/3 = 3/17

1/6+1/12+1/20 nhân 1=(1/6+1/12)+1/20=1/4 +1/20=6/20=3/10

đây nha em.

\(\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}+\dfrac{1}{72}+\dfrac{1}{90}\)

\(=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}+\dfrac{1}{5\cdot6}+\dfrac{1}{6\cdot7}+\dfrac{1}{7\cdot8}+\dfrac{1}{8\cdot9}+\dfrac{1}{9\cdot10}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}+\dfrac{1}{6}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{10}\)

\(=1-\dfrac{1}{10}\)

\(=\dfrac{9}{10}\)

Sai đầu bài nhé, số cuối cùng phải là 110. Giải :

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}+\frac{1}{110}\)

= \(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}+\frac{1}{10.11}\)

=\(\left(\frac{1}{2}-\frac{1}{3}\right)+\left(\frac{1}{3}-\frac{1}{4}\right)+...+\left(\frac{1}{10}-\frac{1}{11}\right)\)

=\(\left(\frac{1}{2}-\frac{1}{11}\right)+0+...+0\)

=\(\frac{9}{22}\)

Mình sửa đề 1 chút nha   

      \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+........+\frac{1}{90}+\frac{1}{110}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{9.10}+\frac{1}{10.11}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)

\(=\frac{1}{2}-\frac{1}{11}\)

\(=\frac{9}{22}\)

   \(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+....+\frac{1}{90}+\frac{1}{110}\)

\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+.....+\frac{1}{9.10}+\frac{1}{10.11}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.......+\frac{1}{9}-\frac{1}{10}+\frac{1}{10}-\frac{1}{11}\)

\(=\frac{1}{2}-\frac{1}{11}\)

\(=\frac{9}{22}\)

\(=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+....+\frac{1}{10\cdot11}\)

\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}\cdot-\frac{1}{11}\)

\(=\frac{1}{2}-\frac{1}{11}\)

\(=\frac{9}{22}\)

\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{90}+\frac{1}{110}\)

= \(\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}+\frac{1}{10.11}\)

= \(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{10}-\frac{1}{11}\)

= \(\frac{1}{2}-\frac{1}{11}+0+...+0\)

= \(\frac{9}{22}\)

: A = 1/6+1/12+1/20+1/30+.........+1/210

A = 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + ... + 1/14.15

A = 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + ... + 1/14 - 1/15

A = 1/2 - 1/15

A = 13/30

Ta có: 1/2= 1/1- 1/2 
1/6= 1/2 - 1/3 
1/12= 1/3- 1/4 
... 
1/30= 1/5 - 1/6 
1/42= 1/6 - 1/7 
Thay vào tổng kia: 1/2+1/6+...+1/30+1/42= 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/5 - 1/6 + 1/6 - 1/7 = 1/2 - 1/7= 5/14 
Chúc bạn học tốt. Thân!

ể! Hai câu trả lời khác nhau mình nên nghe ai đây?

Nhưng mà cũng cảm ơn 2 bạn nhiều nha