Bài 1: Tìm x biết:
2 $\frac{2}{1.3}$ + $\frac{2}{3.5}$ + $\frac{2}{5.7}$ +…+ $\frac{2}{x(x+2)}$= $\frac{2015}{2016}$
Bài 1: Tìm x biết: 2 $\frac{2}{1.3}$ + $\frac{2}{3.5}$ + $\frac{2}{5.7}$ +…+ $\frac{2}{x(x+2)}$= $\frac{2015}{2016}$
By Josie
By Josie
Bài 1: Tìm x biết:
2 $\frac{2}{1.3}$ + $\frac{2}{3.5}$ + $\frac{2}{5.7}$ +…+ $\frac{2}{x(x+2)}$= $\frac{2015}{2016}$
`2/1.3 + 2/3.5 + 3/5.7 + …. + 2/(x(x+2)) = 2015/2016`
`1/1 – 1/3 + 1/3 – 1/5 +…+ 1/x – 1/(x+2) = 2015/2016`
`1/1 – 1/(x+2) = 2015/2016`
`1/(x+2) = 1/1 – 2015/2016`
`1/(x+2) = 1/2016`
`=> x+2 =2016`
`=> x= 2016-2`
`=> x= 2014`
Vậy `x= 2014`
Đáp án + Giải thích các bước giải:
`2/1.3+2/3.5+2/5.7+…+2/(x(x+2))=2015/2016`
`=>1-1/3+1/3-1/5+1/5-1/7+…+1/x-1/(x+2)=2015/2016`
`=>1-1/(x+2)=2015/2016`
`=>1/(x+2)=1-2015/2016`
`=>1/(x+2)=2016/2016-2015/2016`
`=>1/(x+2)=1/2016`
`=>x+2=2016`
`=>x=2016-2`
`=>x=2014`
Vậy `x=2014`