Question

Tính nhanh :

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

 

Answer 1

\(=\frac{1}{1}-\frac{1}{7}=\frac{6}{7}\)

Answer 2

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

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

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

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

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

Answer 3

\(\frac{1}{2}+\frac{1}{6}+...+\frac{1}{42}=\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{6\cdot7}\)

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

\(=\left(\frac{7}{7}-\frac{1}{7}\right)+0+...+0=\frac{6}{7}\)

Answer 4

Đặt biểu thức trên = A. Ta có:

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

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

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

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

Answer 5

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

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

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

= \(\frac{1}{1}-\frac{1}{7}=\frac{6}{7}\)

                  Đáp số: \(\frac{6}{7}\)

Answer 6

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

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

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

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

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

Answer 7

6/7 nhe ban

h minh di roi minh h lai

Answer 8

1/2+1/6+1/12+1/20+1/30+1/42 
= 1/1 x 2 + 1/2 x 3 + 1/3 x 4 + 1/4 x 5 + 1/5 x 6 + 1/6 x 7 
=(1-1/2)+(1/2-1/3)+....+(1/6-1/7) 
=1-1/2+1/2-1/3+....+1/6-1/7 
=1-1/7=6/7

Answer 9

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

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

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

= \(1-\frac{1}{7}\)

= \(\frac{6}{7}\)

Answer 10

=1/1*2+1/2*3+1/3*4+1/4*5+1/5*6+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

=1/1-1/7

=6/7