Đáp án + Giải thích các bước giải:
`1+1/3+1/6+...+2/(x xx (x+1))=1 2009/2010`
`2/2+2/6+2/12+...+2/(x xx (x+1))=4019/2010`
`2/(1xx2)+2/(2xx3)+2/(3xx4)+...+2/(x xx (x+1))=4019/2010`
`2xx(1/(1xx2)+1/(2xx3)+1/(3xx4)+...+1/(x xx (x+1)))=4019/2010`
`2xx(1-1/2+1/2-1/3+1/3-1/4+...+1/x-1/(x+1))=4019/2010`
`2xx(1-1/(x+1))=4019/2010`
`1-1/(x+1)=4019/2010:2`
`1-1/(x+1)=4019/2010. 1/2`
`1-1/(x+1)=4019/4020`
`1/(x+1)=1-4019/4020`
`1/(x+1)=4020/4020-4019/4020`
`1/(x+1)=1/4020`
`x+1=4020`
`x=4020-1`
`x=4019`