* ĐK: \(x\ne0\)

Đề ra ...<=> \(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{1}{x\left(x+1\right)}=\frac{2}{9}\)

<=> \(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{2}{x\left(x+1\right)}=\frac{1}{9}\)

<=> \(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{x\left(x+1\right)}+\frac{1}{x\left(x+1\right)}=\frac{1}{9}\)

<=>\(\frac{1}{6}-\frac{1}{x+1}+\frac{1}{x\left(x+1\right)}=\frac{1}{9}\)

<=>\(\frac{1}{x+1}\left(1-\frac{1}{x}\right)=\frac{1}{6}-\frac{1}{9}\)

<=> \(\frac{x-1}{x\left(x+1\right)}=\frac{1}{36}\)

<=> \(\frac{x-1}{x\left(x-1\right)}=\frac{x-1}{36.\left(x-1\right)}\)

=> x(x-1) = 36. (x-1) => x =36

\(\frac{2}{2}.\left(\frac{1}{21}+\frac{1}{28}+\frac{1}{36}+...+\frac{2}{x+\left(x+1\right)}\right)=\frac{2}{9}\)

\(2\left(\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+...+\frac{1}{x.\left(x+1\right)}\right)=\frac{2}{9}\)

\(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{x.\left(x+1\right)}=\frac{1}{9}\)

\(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{x}-\frac{1}{x+1}=\frac{1}{9}\)

\(\frac{1}{6}-\frac{1}{x+1}=\frac{1}{9}\)

\(\frac{1}{x+1}=\frac{1}{6}-\frac{1}{9}\)

\(\frac{1}{x+1}=\frac{1}{18}\)

x+1=18

x=18-1

x=17

\(\frac{2}{42}+\frac{2}{56}+\frac{2}{72}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)

\(\frac{2}{6.7}+\frac{2}{7.8}+\frac{2}{8.9}+...+\frac{2}{x\left(x+1\right)}=\frac{2}{9}\)

\(\frac{1}{6.7}+\frac{1}{7.8}+\frac{1}{8.9}+...+\frac{1}{x\left(x+1\right)}=\frac{1}{9}\)

\(\frac{1}{6}-\frac{1}{\left(x+1\right)}=\frac{1}{9}\)

\(\frac{1}{\left(x+1\right)}=\frac{1}{6}-\frac{1}{9}=\frac{1}{18}\Leftrightarrow x+1=18\Leftrightarrow x=17\)

=>2/42+2/56+2/72+...+2/(x.(x+1))=2/9

=>2/(6*7)+2/(7*8)+2/(8*9)+......+2/((x+(x+1))=2/9

=>1/6-1/7+1/7-1/8+1/8-1/9+....+1/x-1/x+1=2/9

=>1/6-1/x+1=2/9

=>1/x+1=1/6-2/9

Tự làm tiếp nhé 

\(17\)

=2/42+2/56+....+2/x.(x+1)

=2/6.7+2/7.8+.....+2/x.(x+1)

=2.(1/6.7-1/7.8+....+1/x.(x+1)

=2.(1/6-1/7+1/7-1/8+...+1/x-1/x+1)

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

=2.(x-5/6x+6)

=2x-10/6x+6

bn vt thieu de nha = bao nhieu bn tu tinh 

nhân 2 cả tử và mẫu lên=> ta có 2/6.7 + 2/7.8........

tự làm nốt nhé ;-)

\(\frac{1}{21}+\frac{1}{28}+...+\frac{2}{x\left(x+1\right)}\)

\(=\frac{2}{42}+\frac{2}{56}+...+\frac{2}{x\left(x+1\right)}\)

\(=2\left(\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{x\left(x+1\right)}\right)\)

\(=2\left(\frac{1}{6}-\frac{1}{x+1}\right)\)

\(=2\left(\frac{x-5}{6x+6}\right)=\frac{2\left(x+5\right)}{2\left(3x+3\right)}=\frac{x+5}{3x+3}\)

a)\(\frac{2}{42}+\frac{2}{56}+...+\frac{2}{x\left(x+2\right)}=\frac{2}{9}\)

\(2\left(\frac{1}{6.7}+\frac{1}{7.8}+...+\frac{1}{x\left(x+2\right)}\right)=\frac{2}{9}\)

\(2\left(\frac{1}{6}-\frac{1}{7}+\frac{1}{7}-\frac{1}{8}+...+\frac{1}{x}-\frac{1}{x+2}\right)=\frac{2}{9}\)

\(\frac{1}{6}-\frac{1}{x+2}=\frac{2}{9}:2\)

\(\frac{1}{x+2}=\frac{1}{6}-\frac{1}{9}\)

\(\frac{1}{x+2}=\frac{1}{18}\)

=>x+2=18

=>x=16

b tương tự nhân nó với 1/2

Cám ơn bạn