$\frac{2}{3}$ + $\frac{2}{3^2} $ + $\frac{2}{3^3}$ + $\frac{2}{3^4}$ + ….+ $\frac{2}{3 ^2012}$
$\frac{2}{3}$ + $\frac{2}{3^2} $ + $\frac{2}{3^3}$ + $\frac{2}{3^4}$ + ….+ $\frac{2}{3 ^2012}$
By Valerie
By Valerie
$\frac{2}{3}$ + $\frac{2}{3^2} $ + $\frac{2}{3^3}$ + $\frac{2}{3^4}$ + ….+ $\frac{2}{3 ^2012}$
Đáp án:
`1-1/3^2012`
Giải thích các bước giải:
`2/3+2/3^2+2/3^3+…+2/3^2012`
`=2.(1/3+1/3^2+1/3^3+…+1/3^2012)`
Đặt `A= 1/3+1/3^2+1/3^3+…+1/3^2012`
`3A=1+1/3+1/3^2+…+1/3^2011`
`3A-A=2A=1-1/3^2012`
`A=(1-1/3^2012)/2`
`=2.(1-1/3^2012)/2=1-1/3^2012`
`A = 2/3 + 2/3^2 + 2/3^3 + … + 2/3^2018`
`⇒ 3A = 2 + 2/3 + 2/3^2 + … + 2/3^2017`
`⇒ 3A – A = (2 + 2/3 + … + 2/3^2017) – (2/3 + 2/3^2 + … + 2/3^2018)`
`⇒ 3A – A = 2 – 2/3^2018`
`⇒ 2A = 2 – 2/3^2018`
`⇒ A = (2 – 2/3^2018) : 2`