Tìm x :1/2 + 1/6 + 1/12 + 1/ 20 +…+1/x(x+1)=2020/2021 10/08/2021 Bởi Cora Tìm x :1/2 + 1/6 + 1/12 + 1/ 20 +…+1/x(x+1)=2020/2021
Đáp án: `x=2020` Giải thích các bước giải: `1/2 + 1/6 + 1/12 + 1/ 20 +…+1/(x(x+1))=2020/2021` `=>1/1.2+1/2.3+1/3.4+1/4.5+…+1/(x(x+1))=2020/2021` `=>1-1/2+1/2-1/3=1/3-1/4+1/4-1/5+…+1/x-1/(x+1)=2020/2021` `=>1-1/(x+1)=2020/2021` `=>1/(x+1)=1-2020/2021` `=>1/(x+1)=1/2021` nên : `x+1=2021` `=>x=2021-1` `=>x=2020` Bình luận
Đáp án + Giải thích các bước giải: `1/2 + 1/6 + 1/12 + 1/ 20 +…+1/(x(x+1))=2020/2021` `=>1/1.2+1/2.3+1/3.4+1/4.5+…+1/(x(x+1))=2020/2021` `=>1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+…+1/x-1/(x+1)=2020/2021` `=>1/1-1/(x+1)=2020/2021` `=>1/(x+1)=1/1-2020/2021` `=>1/(x+1)=2021/2021-2020/2021` `=>1/(x+1)=1/2021` `=>x+1=2021` `=>x=2021-1` `=>x=2020` Bình luận
Đáp án:
`x=2020`
Giải thích các bước giải:
`1/2 + 1/6 + 1/12 + 1/ 20 +…+1/(x(x+1))=2020/2021`
`=>1/1.2+1/2.3+1/3.4+1/4.5+…+1/(x(x+1))=2020/2021`
`=>1-1/2+1/2-1/3=1/3-1/4+1/4-1/5+…+1/x-1/(x+1)=2020/2021`
`=>1-1/(x+1)=2020/2021`
`=>1/(x+1)=1-2020/2021`
`=>1/(x+1)=1/2021`
nên : `x+1=2021`
`=>x=2021-1`
`=>x=2020`
Đáp án + Giải thích các bước giải:
`1/2 + 1/6 + 1/12 + 1/ 20 +…+1/(x(x+1))=2020/2021`
`=>1/1.2+1/2.3+1/3.4+1/4.5+…+1/(x(x+1))=2020/2021`
`=>1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+…+1/x-1/(x+1)=2020/2021`
`=>1/1-1/(x+1)=2020/2021`
`=>1/(x+1)=1/1-2020/2021`
`=>1/(x+1)=2021/2021-2020/2021`
`=>1/(x+1)=1/2021`
`=>x+1=2021`
`=>x=2021-1`
`=>x=2020`