1/21+1/28+1/36+...+2/x(x+1)=2/9

=>1/3.7+1/4.7+1/4.9+...+2/x.(x+1)=2/9

=>2/2.3.7+2/2.4.7+2/2.4.9+...+2/x.(x+1)=2/9

=>2/6.7+2/7.8+2/8.9+...+2/x.(x+1)=2/9

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

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

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

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

=>1/x+1=1/18

=>x+1=18

=>x=18-1

=>x=17

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:\(x=17\)