: 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

a) 39                    b) 20                        c) 29                       d) ...

em lớp 6  nha

B= 1/2 + 1/6 + 1/12 +1/20 + 1/30 + 1/42 + 1/56 + 1/72

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

B=1-1/2+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

B=1+0-0-0-0-0-0-0-1/9

B=1-1/9

B=8/9

k em nha

phần A em chịu

còn câu dưới đó e

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

A = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8

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

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

A = 1 + 0 + 0 + 0 + 0 + 0 + 0 - 1/8

A = 1 - 1/8

A = 7/8

* Sửa đề tí nhé 

B = 3/2 - 5/6 + 7/12 - 9/20 + 11/30 - 13/42 + 15/56

B = 3/1.2 - 5/2.3 + 7/3.4 - 9/4.5 + 11/5.6 - 13/6.7 + 15/7.8

B = 3 - 3/2 - 5/2 - ( -5/3 ) + 7/3 - 7/4 - 9/4 - ( -9/5 ) + 11/5 - 11/6 - 13/6 - ( -13/7 ) + 15/7 - 15/8

B = 3 - 3/2 - 5/2 + 5/3 + 7/3 - 7/4 - 9/4 + 9/5 + 11/5 - 11/6 - 13/6 + 13/7 + 15/7 - 15/8

B = 3 + ( -3/2 - 5/2 ) + ( 5/3 + 7/3 ) + ( -7/4 - 9/4 ) + ( 9/5 + 11/5 ) + ( -11/6 - 13/6 ) + ( 13/7 + 15/7 ) - 15/8

B = 3 + -4 + 4 + -4 + 4 + -4 + 4 - 15/8

B = 3 + 0 + 0 + 0 - 15/8

B = 3 - 15/8

B = 9/8

6/7 đó nha bạn

Ta có: 1/2+1/6+1/12+1/20+1/30+1/42=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7=1-1/7=6/7

Đáp số: 6/7

6/7 nha                   

Ta có

\(\frac{1}{2}=\frac{1}{1.2};\frac{1}{6}=\frac{1}{2.3};\frac{1}{12}=\frac{1}{3.4};\frac{1}{20}=\frac{1}{4.5};\frac{1}{30}=\frac{1}{5.6};\frac{1}{42}=\frac{1}{6.7}\)

\(\Rightarrow A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

Ta thấy:

\(\frac{1}{1.2}=1-\frac{1}{2};\frac{1}{2.3}=\frac{1}{2}-\frac{1}{3};...;\frac{1}{6.7}=\frac{1}{6}-\frac{1}{7}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{6}-\frac{1}{7}\)

Thấy

\(-\frac{1}{2}+\frac{1}{2}=0;-\frac{1}{3}+\frac{1}{3}=0;...;-\frac{1}{6}+\frac{1}{6}=0\)

Ta coi như hết

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

          \(=\frac{6}{7}\)

`A=1/2+1/6+1/12+1/20+1/30+...+1/9900`

`=1/(1xx2)+1/(2xx3)+1/(3xx4)+1/(4xx5)+1/(5xx6)+...+1/(99xx100)`

`=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/99-1/100`

`=1/1-1/100`

`=100/100-1/100`

`=99/100`

$A=1/2+1/6+1/12+1/20+1/30+...+1/9900$

$=1/(1xx2)+1/(2xx3)+1/(3xx4)+1/(4xx5)+1/(5xx6)+...+1/(99xx100)$

$=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/99-1/100$

$=1/1-1/100$

$=100/100-1/100$

$=99/100$

 Đặt biểu thức cần tính là A. Ta có : 
A = 9/10 -( 1/90 + 1/72 + ... + 1/2) 
= 9/10 - { 1/( 9.10) + 1/(9.8) + ... + 1/( 2.1)} 
= 9/10 - ( 1/9 - 1/10 + 1/8 - 1/9 + ...+ 1 - 1/2) ( 1/90 = 1/(9.10) = 1/9 - 1/10) 
= 9/10 - ( 1 - 1/10)