Toán $\frac{1}{3^0}$ +$\frac{1}{3^2}$ + $\frac{1}{3^4}$ +…+$\frac{1}{3^86}$ 03/08/2021 By Adalynn $\frac{1}{3^0}$ +$\frac{1}{3^2}$ + $\frac{1}{3^4}$ +…+$\frac{1}{3^86}$
Giải thích các bước giải: Đặt `A=1/3^0+1/3^2+…+1/3^86` `A=1+1/3^2+…+1/3^86` `=>9A=9+1+…+1/3^84` `=>9A-A=(9+1+…+1/3^84)-(1+1/3^2+…+1/3^86)` `=>8A=9-1/3^86=(3^88-1)/3^86` `=>A=(3^88-1)/8.3^86` Trả lời
Đặt `A = 1/{3^0} + 1/{3^2} + 1/{3^4} + … + 1/{3^{86}}` `⇔ 9A = 9 + 1 + 1/{3^2} + …. + 1/{3^{84}}` `⇔ 9A – A = ( 9 + 1 + 1/{3^2} + …. + 1/{3^{84}})-(1/{3^0} + 1/{3^2} + 1/{3^4} + … + 1/{3^{86}})` `⇔ 8A = 9 – 1/{3^{86}}` `⇔ A = {9-1/{3^{86}}}/{8}`. Trả lời
Giải thích các bước giải:
Đặt `A=1/3^0+1/3^2+…+1/3^86`
`A=1+1/3^2+…+1/3^86`
`=>9A=9+1+…+1/3^84`
`=>9A-A=(9+1+…+1/3^84)-(1+1/3^2+…+1/3^86)`
`=>8A=9-1/3^86=(3^88-1)/3^86`
`=>A=(3^88-1)/8.3^86`
Đặt `A = 1/{3^0} + 1/{3^2} + 1/{3^4} + … + 1/{3^{86}}`
`⇔ 9A = 9 + 1 + 1/{3^2} + …. + 1/{3^{84}}`
`⇔ 9A – A = ( 9 + 1 + 1/{3^2} + …. + 1/{3^{84}})-(1/{3^0} + 1/{3^2} + 1/{3^4} + … + 1/{3^{86}})`
`⇔ 8A = 9 – 1/{3^{86}}`
`⇔ A = {9-1/{3^{86}}}/{8}`.