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

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

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

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

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

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

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

1/2+1/6+1/12+1/20+1/30+1/42=1260/3628800

k mình nha cậuLê Đức Nguyên Khoa

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

\(=\frac{1}{2.1}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

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

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

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

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

     S = \(\frac{1}{1x2}+\frac{1}{2x3}+\frac{1}{3x4}+\frac{1}{4x5}+\frac{1}{5x6}+\frac{1}{6x7}\)

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

    S = \(1-\frac{1}{7}=\frac{6}{7}\)

=1/1*2 + 1/2*3 + 1/3*4 + ........1/6*7

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

1/2 và 1/3 và 1/4 và 1/5 và 1/6 xuất hiện 2 lần gạch cả hai 

Còn lại 1/1 -1/7 = 6/7

1/2+1/6+1/12+1/20+1/30+1/42

=1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 +1/6x7

=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

B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + ... + 1/110

B = 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + .... + 1/10.110

B = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + 1/6 - 1/7 + ... + 1/10 - 1/11

B = 1 - 1/11

B = 10/11

 B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + .... + 1/110

=1/1x2 + 1/2x3 + 1/ 3x4 + 1/4x5 + 1/5 x6 + 1/ 6x 7 +.....+ 1/10 x11

=1-1/2 + 1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7 +......+ 1/10 - 1/11

= 1 + (1/2-1/2)+(1/3-1/3)+(1/4-1/4)+(1/5-1/5)+(1/6-1/6)+.....+(1/10-1/10)-1/11

= 1- 1/11=10/11

Vậy B = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + .... + 1/110 = 10/11

cho mình hoi : 1/2 +1/6 +1/12 +1/30 +.....+1/110

cảm ơn nhé

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

\(=\frac{1}{1\times2}+\frac{1}{2\times3}+...+\frac{1}{6\times7}\)

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

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

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

Kết bạn với mình nha!

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

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

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

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

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

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

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

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

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

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

1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42

= 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/6.7

= 1 - 1/2 + 1/2 - 1/3 + ... + 1/6 - 1/7

= 1 - 1/7

= 6/7

chữ gì đây

1211111121

1212111121

121121112

121111222

C = 1/42 + 1/30 + 1/20 + 1/12 + 1/6 + 1/2

C = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42

C = 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 + 1/6x7

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

C = 1 - 1/7

C = 6/7

Ủng hộ mk nha ^_-

ta nhận thấy

1/2=1-1/2

1/6=1/2-1/3

1/12=1/3-1/4

1/20=1/4-1/5

1/30=1/5-1/6

1/42=1/6-1/7

ta có:

1/2+1/6+1/12+1/20+1/30+1/42

=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

bn tự hiểu nha