CÁC BẠN ƠI GIÚP MÌNH !

BẠN NÀO LÀM ĐƯỢC THÌ MÌNH K CHO NHÉ !

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

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

\(=\frac{1}{7\cdot6}+\frac{1}{6\cdot5}+\frac{1}{5\cdot4}+\frac{1}{4\cdot3}+\frac{1}{3\cdot2}\)

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

\(=\frac{1}{2}-\frac{1}{7}\)

\(=\frac{5}{14}\)

= 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

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

\(=\)\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}+\frac{1}{7.8}\)

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

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

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

Áp dụng công thức \(\frac{a}{b\left(b+a\right)}=\frac{1}{b}-\frac{1}{b+a}\) \(\left(a,b>0\right)\) nhé 

Chúc bạn học tốt ~ 

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

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

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

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

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

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

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

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

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

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

  1/2 + 1/6 + 1/12 + 1/20 + 1/30 [mẫu chung là 60 ]

= 1x30/2x30 + 1x10/6x10 + 1x5/12x5 + 1x3/20x3 + 1x2/30x2

= 30/60 + 10/60 + 5/60 + 3/60 + 2/60

= 50 / 60 [rút gọn = 5/6 ]

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

neu co gi sai sot xin gui lai loi nhan

6/7 day minh vua lam dung ne o violympic do.

k cho minh nha cac ban.

đáp án của bài toán này là 6/7 còn cách làm thì làm như bn Hoang Ha Vy

\(=\left(1-\dfrac{1}{2}\right)+\left(1-\dfrac{1}{6}\right)+\left(1-\dfrac{1}{12}\right)+...+\left(1-\dfrac{1}{90}\right)\\ =\left(1+1+...+1\right)-\left(\dfrac{1}{2}+\dfrac{1}{6}+...+\dfrac{1}{90}\right)\\ =9-\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{9\cdot10}\right)\\ =9-\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{9}-\dfrac{1}{10}\right)\\ =9-\left(1-\dfrac{1}{10}\right)=9-\dfrac{9}{10}=\dfrac{81}{10}\)

A=1/2+ 5/6 + 11/12 + 19/20 + 29 30 + 41/42 + 55/56 + 71/72 + 89/90

81/10

`1/2+2/4+3/6+4/8+5/10+6/12`

`=1/2+1/2+1/2+1/2+1/2+1/2`

`=1/2*6=3`

`1/3+1/4+1/5+8/10+20/15+20/30`

`=(1/3+1/4)+(1/5+4/5)+(4/3+2/3)`

`=7/12+1+2`

`=7/12+3=43/12`

\(\dfrac{1}{2}+\dfrac{2}{4}+\dfrac{3}{6}+\dfrac{4}{8}+\dfrac{5}{10}+\dfrac{6}{12}\)
\(=\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{2}+\dfrac{1}{2}\)
\(=\dfrac{1}{2}\times6=3\)
\(------\)
\(\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{8}{10}+\dfrac{20}{15}+\dfrac{20}{30}\)
\(=\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{5}+\dfrac{4}{5}+\dfrac{4}{3}+\dfrac{2}{3}\)
\(=\left(\dfrac{1}{3}+\dfrac{4}{3}+\dfrac{2}{3}\right)+\left(\dfrac{1}{5}+\dfrac{4}{5}\right)+\dfrac{1}{4}\)
\(=\dfrac{7}{3}+1+\dfrac{1}{4}\)
\(=\dfrac{28}{12}+\dfrac{12}{12}+\dfrac{3}{12}\)
\(=\dfrac{43}{12}\)

`=1/2+1/2+1/2+1/2+1/2+1/2= 1/2 \times 6=3`

`----`

`=1/3+1/4+1/5+4/5+4/3+2/3 =(4/3+2/3+)+(1/5+4/5)+1/3+1/4=2+1+1/3+1/4=3+1/3+1/4=43/12`

Đặt tổng trên là A

A= 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

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

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

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

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

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