Question

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

Answer 1

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