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

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

\(=\frac{11}{20}+\frac{1}{5}+\frac{1}{12}\)

\(=\frac{3}{4}+\frac{1}{12}\)

\(=\frac{10}{12}=\frac{5}{6}\)

= 5 / 6 nhé

bằng 

0.83333333333

nha hok tốt nha

ok nhaaaaaaaa

ok ok

`[-1]/2+[-1]/6+[-1]/12+[-1]/20+[-1]/30+[-1]/42+[-1]/56+[-1]/72+[-1]/90`

`=(-1)(1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90)`

`=(-1)(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10)`

`=(-1)(1-1/10)`

`=(-1). 9/10=-9/10`

A = \(\dfrac{-1}{2}\) + \(\dfrac{-1}{6}\)+ \(\dfrac{-1}{12}\)+ \(\dfrac{-1}{20}\)+ \(\dfrac{-1}{30}\)+ \(\dfrac{-1}{42}\)+ \(\dfrac{-1}{56}\)+ \(\dfrac{-1}{72}\)+ \(\dfrac{-1}{90}\)

A = \(\dfrac{-1}{2}\) + \(\dfrac{-1}{2\times3}\)+ \(\dfrac{-1}{3\times4}\)+ \(\dfrac{-1}{4\times5}\)+ \(\dfrac{-1}{5\times6}\)+ \(\dfrac{-1}{6\times7}\)+ \(\dfrac{-1}{7\times8}\)+ \(\dfrac{-1}{8\times9}\)+ + \(\dfrac{-1}{9\times10}\)

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

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

A = \(\dfrac{-9}{10}\)

ok luôn.hay thì like nha

ta có

1/2+1/6+1/12+1/20+1/30+1/42+1/56+1/72

=1/1*2+1/2*3+1/3*4+...+1/8*9

=1-1/2+1/2-1/3+1/3-1/4+...+1/8-1/9

=1-1/9

=8/9

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

\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{7}-\dfrac{1}{8}\)

\(A=1-\dfrac{1}{8}=\dfrac{7}{8}\)

\(A=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}+\dfrac{1}{56}\)

\(A=\dfrac{367}{420}\approx0,87\)

A = 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + 1/42 + 1/56 + 1/72

= 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 + 1/5.6 + 1/6.7 + 1/7.8 + 1/8.9

= 1/1 − 1/2 + 1/2 − 1/3 + 1/3 − 1/4 + 1/4 − 1/5 + 1/5 − 1/6 + 1/6 − 1/7 + 1/7 − 1/8 + 1/8 − 1/9

= 1 − 1/9

= 8/9

E =16+112+120+130+142+156

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

 E=\(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{1}-...+\dfrac{1}{7}-\dfrac{1}{8}\)

 E=\(\dfrac{1}{2}-\dfrac{1}{8}=\dfrac{3}{8}\)

E= \(\dfrac{3}{8}\)

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

\(\Rightarrow x+\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+\dfrac{1}{4\times5}+\dfrac{1}{5\times6}=\dfrac{47}{42}\\ \Rightarrow x+1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{6}=\dfrac{47}{42}\\ \Rightarrow x+1-\dfrac{1}{6}=\dfrac{47}{42}\\ \Rightarrow x=\dfrac{47}{42}-\dfrac{5}{6}=\dfrac{2}{7}\)

\(x=\dfrac{2}{7}\)

2/7 nha

hok tốt

k mik đi

=9/10-(1/2+1/6+...+1/90)

=9/10-(1-1/2+1/2-1/3+...+1/9-1/10)

=9/10-9/10=0

\(B=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}\)

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

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

\(B=1-\dfrac{1}{7}\)

\(B=\dfrac{6}{7}\)

Quy đồng ik em

\(B=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{12}+\dfrac{1}{20}+\dfrac{1}{30}+\dfrac{1}{42}\)

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