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

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

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

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

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

  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 ]

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

= 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

\(\frac{1}{42}+\frac{1}{30}+\frac{1}{20}+\frac{1}{12}+\frac{1}{6}=\frac{1}{6\times7}+\frac{1}{5\times6}+\frac{1}{4\times5}+\frac{1}{3\times4}+\frac{1}{2\times3}\)

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

\(=\frac{1}{2}-\frac{1}{7}=\frac{5}{14}\)

\(\frac{3}{8}\)nha bạn

3/8 đó bạn

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

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

\(\frac{1}{2}-\frac{1}{8}=\frac{4}{8}-\frac{1}{8}=\frac{3}{8}\)

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.

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

\(\text{= 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9 + 1/9.1}\)

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

\(=1/1-1/10-10/10-1/10-9/10\)

Vậy \(\text{ 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72 + 1/90 = 9/10}\)

Sửa đề:

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

\(=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+\dfrac{1}{5.6}+\dfrac{1}{6.7}+\dfrac{1}{7.8}+\dfrac{1}{8.9}+\dfrac{1}{9.10}\)

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

\(=\dfrac{1}{2}-\dfrac{1}{10}\)

\(=\dfrac{3}{5}\)

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

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

   =1/2-1/8=3/8

\(=\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}+\frac{1}{7\cdot8}\)

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

=\(\left(\frac{1}{2}-\frac{1}{8}\right)+\left(\frac{1}{3}-\frac{1}{3}\right)+...+\left(\frac{1}{7}-\frac{1}{7}\right)\)

\(=\left(\frac{1}{2}-\frac{1}{8}\right)+0+...+0\)

\(=\frac{1}{2}-\frac{1}{8}=\frac{4}{8}-\frac{1}{8}=\frac{3}{8}\)

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

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

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

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

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

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