1+1/3+1/6+1/10+…+2/Xx(X+1)=1 và 2009/2010

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`