Đáp án + Giải thích các bước giải:
`1+1/3+1/6+...+2/(x.(x+1))=1-1989/1991`
`=>2/2+2/6+2/12+...+2/(x.(x+1))=1991/1991-1989/1991`
`=>2/1.2+2/2.3+2/3.4+...+2/(x.(x+1))=2/1991`
`=>2(1/1.2+1/2.3+1/3.4+...+1/(x.(x+1))=2/1991`
`=>2(1-1/2+1/2-1/3+1/3-1/4+...+1/x-1/(x+1))=2/1991`
`=>2(1-1/(x+1))=2/1991`
`=>1-1/(x+1)=2/1991:2`
`=>1-1/(x+1)=2/1991. 1/2`
`=>1-1/(x+1)=1/1991`
`=>1/(x+1)=1-1/1991`
`=>1/(x+1)=1991/1991-1/1991`
`=>1/(x+1)=1990/1991`
`=>x+1=1991/1990`
`=>x=1991/1990-1`
`=>x=1991/1990-1990/1990`
`=>x=1/1990`
