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

1/2+1/6+1/12+1/20+1/30+1/42 = \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)

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

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

= \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+\frac{1}{6\cdot7}\)

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

= \(\frac{1}{1}-\frac{1}{7}\)

= \(\frac{7}{7}-\frac{1}{7}\)

= \(\frac{6}{7}\)

Bài 1

\(\dfrac{1}{2}+\dfrac{7}{10}=\dfrac{5}{10}+\dfrac{7}{10}=\dfrac{12}{10}=\dfrac{6}{5}\)

\(\dfrac{8}{15}\times\dfrac{5}{12}=\dfrac{40}{180}=\dfrac{2}{9}\)

Baì 2 

\(30\times\dfrac{5}{3}=50\)

\(\dfrac{6}{5}\times\dfrac{5}{3}=2\)

\(\dfrac{12}{40}\times\dfrac{5}{3}=\dfrac{1}{2}\)

Bài 1:

1/2 + 7/10 = 10/20 + 14/20 = 6/5

8/15 x 5/12 = 2/9

Bài 2: 

5/3 của số 30 là: 30 x 5/3 = 50

5/3 của số 6/5 là: 6/5 x 5/3 = 2

5/3 của số 12/40 là: 12/40 x 5/3 = 1/2

\(\dfrac{1}{2}\)+\(\dfrac{7}{10}\)=\(\dfrac{5}{10}\)+\(\dfrac{7}{10}\)=\(\dfrac{12}{10}\)=\(\dfrac{6}{5}\)

Bài 1:

1/2  +  7/10 = 1, 2 

 8/15   x   5/12 = 2/9

1) 1/2+ 7/10 = 5/10+ 7/10=  12/10 = 6/5

8/15 x 5/12= 40/ 180 = 2/9

2) 5/3 của 30 là: 50

5/3 của 6/5 là: 2

5/3 của 12/40 là: 1/2

1/2  +  7/10 = 6/5

 8/15   x   5/12 = 2/9

\(\left(\frac{19}{13}+\frac{7}{13}\right)+\left(\frac{1}{9}+\frac{17}{9}\right)+\frac{14}{16}\)

=       \(\frac{16}{13}+\frac{18}{9}+\frac{14}{16}\)

= \(\frac{42}{13}+\frac{14}{16}\)

=        \(\frac{427}{104}\)

=(19/13 + 7/13 ) + (14/6 +4/6 ) +(1/9 +17/9 )

=26/13 +18/6 +18/9

=2 +3 + 2

=7

A=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

A=1-1/7=6/7

=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)+(1/2-1/2)+(1/3-1/3) + ... +(1/6-1/6)

= (1-1/7) + 0+...+0 = 1-1/7 = 7/7 - 1/7 = 6/7

Vậy A =6/7

S=1/2+1/6+...............+1/2450

S=1/1.2+1/2.3+............+1/49.50

S=1-1/2+1/2-1/3+..........+1/49-1/50

S=1-1/50

S=49/50

S=1/2+1/6+...............+1/2450

S=1/1.2+1/2.3+............+1/49.50

S=1-1/2+1/2-1/3+..........+1/49-1/50

S=1-1/50

S=49/50

S=1/2+1/6+1/12+1/20+...+1/2352+1/2450

S=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/48-1/49+1/49-1/50

S=1-1/50

S=49/50

Vậy S=49/50

TL

\(\frac{2}{3}-\frac{1}{9}=\frac{18}{9}-\frac{1}{9}=\frac{17}{9}\)

nhaaaaa

HT

TSP

vì 9 chia hết cho 3 nên giữ nguyễn 1/9 và quy đồng 2/3

2/3-1/9= 6/9-1/9=5/9

              đáp án là : 5/9

@@@@@@@@

HT~

2/3-1/9=6/9-1/9=5/9

Bổ sung đề bài : Tính

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

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

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

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