6/7 mình làm rồi 

trên violympic

5/14 đúng chắc luôn

6/7 tick nha nguyễn hoàng anh thư 

gioi qua ban oi

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

\(=\dfrac{1}{182}\)

đúng nè

CÁC BẠN ƠI GIÚP MÌNH !

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

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

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

=1/2 - 1/7 = 5/14

`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`

=(1/1-1/2)+(1/2-1/3)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)                    =(1/2-1/2)+(1/3-1/3)+(1/4-1/4)+(1/5-1/5)+(1/6-1/6)+(1/1-1/7)                                             = 0+0+0+0+0+6/7                       =6/7

\(M=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{6.7}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{6}-\dfrac{1}{7}=1-\dfrac{1}{7}=\dfrac{6}{7}\)

6/7

= 1/1x2+1/2x3+...+1/7x8

= 1-1/2+1/2-...-1/8

= 1-1/8

=7/8

a/ \(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}=\)

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

= 1-1/8 = 7/8

b/ = (17/9+1/9)+(19/13+7/13)+(14/6+10/6) = 18/9 + 26/13 + 24/6 = 2+2+4 = 8

Đặt \(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+......+\frac{1}{56}\)

\(\Rightarrow A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+........+\frac{1}{7.8}\)

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

\(\Rightarrow A=1-\frac{1}{8}\)

\(\Rightarrow A=\frac{7}{8}\)