Tính M= $\frac{1}{1.3}$ + $\frac{1}{3.5}$ + $\frac{1}{5.7}$ + …+ $\frac{1}{2015.2017}$
Tính M= $\frac{1}{1.3}$ + $\frac{1}{3.5}$ + $\frac{1}{5.7}$ + …+ $\frac{1}{2015.2017}$
By Athena
By Athena
Tính M= $\frac{1}{1.3}$ + $\frac{1}{3.5}$ + $\frac{1}{5.7}$ + …+ $\frac{1}{2015.2017}$
`M=1/(1.3)+1/(3.5)+1/(5.7)+…+1/(2015.2017)`
`2M=2/(1.3)+2/(3.5)+2/(5.7)+…+2/(2015.2017)`
`2M=1-1/3+1/3-1/5+1/5-1/7+…+1/2015-1/2017`
`2M=1-1/2017`
`2M=2016/2017`
`M=1008/2017`
Đáp án + giải thích bước giải :
`M = 1/(1 . 3) + 1/(3 . 5) + 1/(5 . 7) + …. + 1/(2015 . 2017)`
`-> 2M = 1 – 1/3 + 1/3 -1/5 + 1/5 – 1/7 + …. + 1/2015 – 1/2017`
`-> 2M = 1 + (- 1/3 + 1/3 -1/5 + 1/5 – 1/7 + …. + 1/2015 ) – 1/2017`
`->2 M = 1 – 1/2017`
`-> 2M = 2017/2017 – 1/2017`
`-> 2M =2016/2017`
`-> M = 2016/2017 : 2`
`-> M =1008/2017`