Ta có: 

1/x - 1/(x+1) = (x + 1 - x)/x(x+1) = 1/x(x+1) 

⇒ 2/x(x+1) = 2/x - 2/(x+1) 

(*) trở thành: 

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

⇔ 2/6 - 2/(x+1) = 2/9 

⇔ 1/6 - 1/(x+1) = 1/9 

⇔ 1/(x+1) = 1/18 

⇔ x + 1 = 18 

⇔ x = 17 

Đáp số: x = 17

đáp số:\(x=17\)

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

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

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

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

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

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

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

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

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

=> x+1=18

x=18-1

x=17

2 / 6,7 + 2 / 7.8 + ... + 2 / x (x + 1) = 2/9 Ta có: 1 / x - 1 / (x + 1) = (x + 1 - x) / x (x 1) = 1 / x (x + 1) ⇒ 2 / x (x + 1) = 2 / x - 2 / (x + 1) (*) trở thành: 2/6 - 2/7 + 2/7 - 2/8 + ... + 2 / x - 2 / (x + 1) = 2/9 ⇔ 2/6 - 2 / (x + 1) = 2/9 ⇔ 1/6 - 1 / (x + 1) = 1/9 ⇔ 1 / (x + 1) = 1/18 ⇔ x + 1 = 18 ⇔ x = 17 Đáp số: x = 17

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

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

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

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

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

\(\frac{1}{x+1}=\frac{1}{6}-\frac{1}{9}=\frac{1}{18}\)

=> x+1 =18

=> x = 18 - 1

=> x = 17